The name "Soma" itself is mystic in nature where multiple things are interrelated within it:
Soma is Lord Shiva along with Uma
The highly auspicious form of Lord Shiva which is accompanied by Uma which removes all misery is known as Soma. Soma = Sa + Uma = He who is with Uma ie. Lord Shiva. Let's look at some references from Harivamsha Parva of Mahabharata:
स्वयं हि दर्शनं तेषां ददौ त्रिपुरनाशनः ।
श्वेतं वृषभमारुह्य सोमः सप्रवरः प्रभुः । 2-82-24
The destroyer of Tripura, the lord (Shiva), appeared in person, mounted on the white bull, accompanied by Uma and all his followers.
उपर्युपरि सर्वेषां सोमदेवो महेश्वरः ।
तस्थावमितविक्रान्तः स्वैर्गणैः परिवारितः ॥ 2-69-5
High above all of them, the great lord Maheswara with Uma, having high valiance, stood there, surrounded by his followers.
मूर्तिमन्तश्च ते वृक्षाः सोमं देवं वृषध्वजम् ।
उपतिष्ठन्ति सततं प्रवरैः सह केशव ॥2-68-25
Keshava! Those trees, in the bodily form, always worship the Lord Shiva along with Uma, having the flag as bull, along with women.
ततः प्राप्तो महादेवः सोमः सप्रवरो विभुः ।
तस्थावुपरि बिल्वस्य तथा गङ्गोदकस्य च ॥2-74-20
Then the lord, the great Lord Shiva, accompanied by Uma and the gaNa attending him arrived there and stood above the water of Ganga and the Bilva fruits.
Thus as clear from above, the highly auspicious Uma Maheswara Swarupa itself is referred to as Soma. Even RigVeda reveals highly auspicious and sin removing nature of Soma-Rudra form:
सोमारुद्रा युवमेतान्यस्मे विश्वा तनूषु भेषजानि धत्तम् ।
अव स्यतं मुञ्चतं यन्नो अस्ति तनूषु बद्धं कृतमेनो अस्मत् ॥३॥
तिग्मायुधौ तिग्महेती सुशेवौ सोमारुद्राविह सु मृळतं नः ।
प्र नो मुञ्चतं वरुणस्य पाशाद्गोपायतं नः सुमनस्यमाना ॥४॥ (RigVeda 6.74)
Provide, O Soma-Rudra, for our bodies all needful medicines to heal and cure us. Set free and draw away the sin committed which we have still inherent in our persons. Armed with keen shafts and weapons, kind and loving, be gracious unto us, Soma-Rudra. Release us from the noose of Varuṇa; keep us from sorrow, in your tender loving-kindness.
Soma form pervades the entire universe.
यल्लिङ्गाङ्कं यच्च लोके भगाङ्कं सर्वं सोम त्वं स्थावरं जङ्गमं च ।
प्राहुर्विप्रास्त्वां गुणिनं तत्त्वविज्ञास्तथा ध्येयामम्बिकां लोकधात्रीम् ॥ (Harivamsha 2-74-32)
O the great lord accompanied by Uma! The fixed and movable entities of this world marked by masculine and feminine genders, are the manifestations of both of you. The wise brahmins, knowledgeable about the principles, call you the one with qualities and worship Ambika, as the mother of the world.
यल्लिङ्गाङ्कं त्र्यम्बकः सर्वमीशो भगलिङ्गाङ्कम् यद्ध्युमा सर्वधात्री ।
नान्यत्तृतीयं जगतीहास्ति किञ्चित्महादेवात्सर्वसर्वेश्वरोऽसौ ॥ (Harivamsha 2-72-60)
All bodies in the world with masculine gender are forms of three-eyed lord shiva. All bodies in the world with feminine gender are forms of universal mother Uma. There is nothing else in the world other than these two. Lord Shiva is the lord of all.
पुल्लिङ्गं सर्वमीशानं स्त्रीलिङ्गं विद्धि चाप्युमाम्।
द्वाभ्यां तनुभ्यां व्याप्तं हि चराचरमिदं जगत्।। (Mahabharata 13-45-219)
All masculine principles are Lord Ishana, all feminine principles are Goddess Uma. These two bodies have filled the entire Universe.
Vedas also say that Soma pervades the entire Universe and is originator of all Gods also:
स्वायुधः पवते देव इन्दुरशस्तिहा वृजनं रक्षमाणः । पिता देवानां जनिता सुदक्षो विष्टम्भो दिवो धरुणः पृथिव्याः ॥ (RigVeda 9.87.2) सोमः पवते जनिता मतीनां जनिता दिवो जनिता पृथिव्याः । जनिताग्नेर्जनिता सूर्यस्य जनितेन्द्रस्य जनितोत विष्णोः ॥ (RigVeda 9.96.5)
Soma, the well-armed God, is flowing onward, who quells the curse and guards from the treacherous onslaught, Father, begetter of the Gods, most skillful, the buttress of the heavens and earth's supporter. Father of holy hymns, Soma flows onward the Father of the earth, Father of heaven: Father of Agni, Surya's generator, the Father who begat Indra and Vishnu.
In the Bhasma Jabala Upanishad Lord Shiva himself explains RigVeda 9.96.5 as:
ब्रह्म सोमोऽहं पवनः सोमोऽहं पवते सोमोऽहं
जनिता मतीनां सोमोऽहं जनिता पृथिव्याः सोमोऽहं
जनिताऽग्नेः सोमोऽहं जनिता सूर्यस्य सोमोऽहं
जनितेन्द्रस्य सोमोऽहं जनितोत विष्णोः सोमोऽहमेव
जनिता स यश्चन्द्रमसो देवानां भूर्भुवस्वरादीनां
सर्वेषां लोकानां च । विश्वं भूतं भुवनं चित्रं
बहुधा जातं जायमानं च यत्सर्वस्य सोमोऽहमेव
जनिता विश्वाधिको रुद्रो महर्षिः । (BhasmaJabala Upanishad)
I, Soma, am Brahman; I Soma (with Uma), am Vayu; I Soma, am that which is pervading through all. I am the creator of the senses. I, Soma, am the creator of the Earth. I, Soma, am the creator of the Fire, the Sun, Indra, Vishnu, the Moon, the Devas, and all the worlds – Bhuh, Bhuvah, Suvah, and others. I, Soma, am the creator of various worlds, past, present, and future. I, Rudra the great seer transcending all, see the Brahma and other created beings.
Shiva Purana also contains Upabrahmanam of RigVeda 9.96.5 and explains how Soma is the originator of Gods:
दृष्टो रुद्रेण देवो ऽसावसृजद्विश्वमीश्वरः ॥ ७.२,८.११
वर्णाश्रमव्यवस्थां च चकार स पृथक्पृथक् ॥ ७.२,८.११
सोमं ससर्ज यज्ञार्थे सोमाद्द्यौस्समजायत ॥ ७.२,८.१२
धरा च वह्निः सूर्यश्च यज्ञो विष्णुश्शचीपतिः ॥ ७.२,८.१२
ते चान्ये च सुरा रुद्रं रुद्राध्यायेन तुष्टुवुः ॥ ७.२,८.१३
प्रसन्नवदनस्तस्थौ देवानामग्रतः प्रभुः ॥ ७.२,८.१३
अपहृत्य स्वलीलार्थं तेषां ज्ञानं महेश्वरः ॥ ७.२,८.१४
तमपृच्छंस्ततो देवाः को भवानिति मोहिताः ॥ ७.२,८.१४ (Shiva Purana)
Brahmā viewed by Rudra created the universe. He prescribed the rules for different bastes and stages of life separately. For the sake of sacrifice he created Soma. From Soma was born the heaven, earth, fire, sun, sacrifice, Viṣṇu and Indra. They and the gods eulogized Rudra with the hymns dedicated to him. The Lord stood before the gods with his face beaming with delight. The Lord took away their knowledge, sportively. The deluded gods asked him, “Who are you Śir?”
Then Lord Shiva explains how he is the Supreme Brahman and this event is the same which is also described in Atharvasiras Upanishad.
-- The AgniSoma principle:
Soma form which is Lord Shiva along with Uma can also be called as SomaRudra which means "Rudra who is with Uma". By the Vedic statements like "rudro vA esHa yad agnis" (Rudra himself is Agni: YajurVeda 5.5.7), "Rudraya namostwo Agnaye..." etc... Rudra can also be called Agni. So the SomaRudra principle can also be called as SomaAgni or more appropriately AgniSoma which is called by scripture. In Mahabharata, Lord Krishna himself tells that half of Lord Shiva's body is Agni and half is Soma:
द्वे तनू तस्य देवस्य वेदज्ञा ब्राह्मणा विदुः।
घोरामन्यां शिवामन्यां ते तनू बहुधा पुनः।।
उग्रा घोरा तनुर्याऽस्य सोऽग्निर्विद्युत्स भास्करः।
शिवा सौम्या च या त्वस्य धर्मस्त्वापोथ चन्द्रमाः।।
आत्मनोऽर्धं तु तस्याग्निः सोमोऽर्धं पुनरुच्यते। (Mahabharata 13-266)
Brahmanas conversant with the Vedas say that that god has two forms. One of these is terrible, and the
other mild and auspicious. Those two forms, again, are subdivided into many forms. That form which is
fierce and terrible is regarded as identical with Agni and Vidyuta and Surya. The other form which is
mild and auspicious is identical with Righteousness and water and Chandramas. Then, again, it is said
that half his body is Agni and half is Soma.
Lord Shiva himself in Shiva Purana says to Uma:
अहमग्निशिरोनिष्ठस्त्वं सोमशिरसि स्थिता ॥ ७.१,२७.१३
अग्नीषोमात्मकं विश्वमावाभ्यां समधिष्ठितम् ॥ ७.१,२७.१३ (Shiva Purana)
I am stationed on the head of Agni. You are stationed on the head of Soma. This universe in the form of “Agnīṣoma” is presided over by us both.
Again the Shiva Purana explains the AgniSoma principle in the next chapter:
अग्निरित्युच्यते रौद्री घोरा या तैजसी तनुः ॥ ७.१,२८.३
सोमः शाक्तो ऽमृतमयः शक्तेः शान्तिकरी तनुः ॥ ७.१,२८.३ (Shiva Purana)
The body of Rudra which is fiery and terrible is called Agni. The Soma pertains to Shakti. It is nectarine and is the body of Shakti that causes calmness.
Agni produces Soma (Amrita) and again Agni burns with the help of Amrita (Soma). This is the eternal principle as described by Shiva Purana as:
अग्नेरमृतनिष्पत्तिरमृतेनाग्निरेधते ॥ ७.१,२८.७
अत एव हि विक्रान्तमग्नीषोमं जगद्धितम् ॥ ७.१,२८.७
हविषे सस्यसम्पत्तिर्वृष्टिः सस्याभिवृद्धये ॥ ७.१,२८.८
वृष्टेरेव हविस्तस्मादग्नीषोमधृतं जगत् ॥ ७.१,२८.८
अग्निरूर्ध्वं ज्वलत्येष यावत्सौम्यं परामृतम् ॥ ७.१,२८.९
यावदग्न्यास्पदं सौम्यममृतं च स्रवत्यधः ॥ ७.१,२८.९
अत एव हि कालाग्निरधस्ताच्छक्तिरूर्ध्वतः ॥ ७.१,२८.१० (Shiva Purana)
Amṛita issues from Agni. Agni increases through Amṛita. The powerful AgniSoma is beneficent to the universe. The luxuriant growth of Vegetation is for the Havis. The rain contributes to the flourishing growth of vegetation. So Havis is the outcome of rain, the universe is sustained by AgniSoma. The Agni blazes upwards as far as the great Amrita of Soma. The Amrita of Soma flows as far as the support of Agni. That is why the Kalagni stays below and the Shakti upwards. The upward blazing is till burning and the downward flow is till complete drenching.
Vedas also speak of this AgniSoma principle. In AtharvaVeda Lord Shiva himself tells that he is the controller of the AgniSoma principle:
अहं जजान पृथिवीमुत द्यामहमृतूरजनयं सप्त सिन्धुन्।
अहं सत्यमनृतं यद् वदामि यो अग्नीषोमावजुषे सखाया।। (AtharvaVeda 6.61)
I am the originator of Earth, Heavens and Seven Rivers. What I speak that is the Truth, I conjoin Agni and Soma together.
Lord Rudra himself is the Rishi of the above mantra so it is he himself who is speaking it. Lord Shiva being the controller of AgniSoma principle is also seen in YajurVeda, where during Tripura Samhara the arrow was formed using AgniSoma principle and it was Lord Shiva himself who shot it:
तेषामसुराणां तिस्त तिस्त्रः पुर आसन्नयस्मय्यवमाथ रजताथ हरिणी ता देवा जेतुं नाशक्नुवन्ता उपसदैवाजिगीषन्तस्मादाहुर्यश्चैव वेद यश्च नोपसदा वै महापुरं जयन्तीति त इषु समस्कुर्वताग्निमनीकं सोमं शल्यं विष्णुं तेजनं तेऽब्रुवन्क इमामसिष्यतीति रुद्र इत्यब्रुवन्रुद्रो वै क्रुरः सोऽस्यत्विति सोऽब्रवीद्वरंवृणा अहमेव पशूनामधिपतिरसानीति तस्माद्रुद्र पशूनामधिपतिस्ता रुद्रोऽवासृजत्स तिस्त्रः पुरो भित्वैभ्यो..... [YajurVeda 6.2.3 ]
The Asuras had Tripuras; the lowest was of iron, then there was one of silver, then one of gold. The gods could not conquer them; they sought to conquer them by siege; therefore they say--both those who know thus and those who do not--'By siege they conquer great citadels.' They made ready an arrow, Agni as the point, Soma as the socket, Visnu as the shaft. They said, 'Who shall shoot it?' 'Rudra', they said, 'Rudra is fierce, let him shoot it.' He said, 'Let me choose a boon; let me be overlord of Pashus.' Therefore is Rudra overlord of Pashus. Rudra let it go; it cleft the Tripuras and drove the Asuras away from these worlds.
-- Soma as Moon is also a form of Shiva:
Moon is also called Soma and the property of Moon also matches Gunas like coolness, exuding Amrita, blissful light, etc...
स वै त्वम् इत्य् अब्रवीद् रुद्र एव इति । यद् रुद्रश् चन्द्रमास् तेन । (RigVeda Kausitki Brahmana Chapter 6) .... तमब्रवीन्महान्देवोऽसीति । तद्यदस्य तन्नामाकरोच्चन्द्रमास्तद्रूपमभवत्प्रजापतिर्वै चन्द्रमाः प्रजापतिर्वैमहान्देवः (YajurVeda Shatapatha Brahmana 6.1.3)
He answered, ‘You are Rudra.’ Since the moon is Rudra, thereby Rudra harms him not, nor his offspring, nor his cattle, nor any one claiming to he his.... He said to him, 'You are MahaDeva.' And because he gave him that name, the moon became suchlike, for the moon is Prajapati, and Prajapati is Mahadeva.
Itihasas and Puranas also describe the above thing and mention Soma (moon here) is also form of Shiva:
भूमिरापोऽनलो वायुः खं सूर्यश्च तथा शशी ।
अग्निश्च यजमानश्च प्रकृतिश्चैवमष्टधा ॥३-८५-२१ (Harivamsha) ....
सूर्यों जल मही वहिर्वायुराकाशमेव च।
दीक्षितो ब्राह्मणः सोम इत्येतास्तनवः क्रमात्॥७॥ (Vishnu Purana 1.8)
he earth, water, fire, wind, sky, sun as well as moon and the god of fire as the institutor of the sacrifice (yajamAna) -- These are the eight-fold natural forms of the Lord.... He also assigned to them their respective stations, the Sun, water, ether, air, fire, earth, the ministrant Brahman, and the moon; for these are their several forms.
-- Soma as Nectar / Amrita / Drink:
Getting Darshana of Lord Rudra is itself drinking of Soma. In Atharvasiras when Gods get to know the real nature of Lord Shiva after being explained by Lord Shiva himself, they say explaining RigVeda 8.48.3:
अपाम सोमममृता अभूमागन्म ज्योतिरविदाम देवान् ।
किं नूनमस्मान्कृणवदरातिः किमु धूर्तिरमृतं मार्त्यस्य ।
सोमसूर्यपुरस्तात् सूक्ष्मः पुरुषः । (Atharvasiras Upanishad)
We have drunk the Soma Amrita; we have become immortal; we have gone to the light; we have found the gods. What can hostility do to us now, and what the malice of a mortal, o immortal one? You who are primeval are older than the sun and the moon.
Soma (moon) which is on the head of Lord Shiva also exudes Amrita (Soma), which is discussed here:
अथारुह्य हरस्यांगं गलमावेष्ट्य संस्थितः |
तस्य निश्वासपवनैरथ जातो हुताशनः || ३० ||
तस्योष्मणा चंद्र लेखा जटाजूटाटवी स्थिता |
सार्द्रतां तु तदा सायात्प्लावितं तद्वपुर्यथा || ३१ ||
हरमौलिकपालानामभूत्संजीविता तदा || ३२ ||
पपाठ पूर्वमभ्यस्तं सर्वयोगश्रुतिक्रमम् |
श्रुत्वा परस्पराधीतं विवदंति शिरांस्यथ || ३३ || (Padma Purana 6.10)
Vasuki ejected, through his fear, the tail of the mouse, which he had seized; and then mounting upon Shiva's body, he encircled his neck and remained there. Due to its heat, the crescent moon remained in the forest of his matted hair. She (i.e. the crescent moon) then became wet, and bathed his body with Amrita (ambrosia); the row of the skulls on Shiva's head was brought back to life. And they recited all the sacred texts in due order, which they had formerly studied. The heads, hearing recital (of the sacred text) done by one another, discussed it.
The AgniSoma principle which was discussed earlier is also in play in the above story. Moon also helps in the growth of Soma plants which are used in sacrifices like Soma Yajna.
Sayana in his Bhasya of Sri Rudram tells that:
नमः सोमाय चेति। उमया सह वर्तते इति सोमः।
Now Namaha Somaya: He is along with Uma thus called Soma
Abhinava Shankara in his Bhasya of Sri Rudram tells:
एतदेवोपपादयितुं नमः सोमायेति विशेषितमा; उमया सहित: सोम:, उमेति प्रणववर्णव्यत्यासरुपः "पराशक्ति: प्रणव" इति लैङ्गादिषु प्रतिपादितं....
Now the special "Namaha Somaya"; He who is with Uma: Thus Soma; Uma is in the form of varnas of Pranava. She is "Parashakti Pranava" as established by texts like Linga Purana...
Adi Shankara while explaining the name Soma of Vishnu Sahasranama says:
सोमरुपेणौषधीः पोषयन् सोमः उमया सहितः शिवो वा। (Shankaracharya Vishnu Sahasranama Bhasya)
Soma: Nourishing the plants in the form of Moon, or Soma means Shiva who is ever with Uma.
Lord Kartikeya in his Sri Rudram Bhasya available in Shiva Rahasya correlates various things related to Soma very nicely as:
तस्मै देव नमोऽस्तु यः करुणया प्रादुर्भवन्नग्रतो। भक्तान् पाति सहोमया प्रतिदिनं देवान् पितृन्मानवान्।। अन्यानप्यमृतेन तर्पयति यः सोमात्मना यज्वनः। सर्वानभ्युदयेन योजयति यः सोमादियागात्मना। यश्च द्रावयति स्वयं प्रणमतां नित्यं रुजं योगिनां।
Salutation to that Lord who out of compassion, appear before them along Uma and protect the devotees- the Gods, the Pitrus, human beings and others -- everyday. You satisfy them with nectar through your form of Soma, the moon; and also lead the sacrifiers to prosperity through your form of Soma Yaga and other Yajnas. We offer our salutations to you who are engaged in driving away the afflictions of the devotees and Yogins.
By summarizing above writing we can say:
Soma (Shiva with Uma) pervades the entire universe. Soma (Shiva) becomes Soma (Moon). Soma (Shiva) wears Soma (Moon). Soma (Moon) produces Soma (Amrita). Soma (Amrita) bathes Soma (Shiva). Soma (Moon) grows Soma (plant). Soma (plant) through sacrifice becomes Soma (Amrita). Agni produces Soma (nectar/rain) by Yajna, Soma (ghee/plants) again helps to maintain Agni. The entire Universe is AgniSoma or SomaRudra or simply Soma.