Why there's a crescent moon over lord Shiva's head?
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First we should know that Moon itself is a form of lord Shiva through his Ashtamurti form! As described in the answer there, Kaushitki Brahmana of the RigVeda (chapter 6) itself states:
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
The Shatapatha Brahamana of YajurVeda (6th Kanda 3rd Brahamana) too states:
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.
So, the Moon is very closely related to Lord Shiva. In other words wearing moon means Lord Shiva wearing a reflection of himself. But still all these Vedic truths manifests through various incarnations and leelas of Lord Shiva in the physical form which are described in the stories present in the Itihasas and Puranas. In the Skandha Purana (Prabhasha Kshetra 1.18), Devi Parvati asks this same question to Lord Shiva:
॥ देव्युवाच ॥ ॥
अयं यो वर्त्तते देव चंद्रस्ते शिरसि स्थितः ॥
कस्यायं कथमुत्पन्नः कस्मिन्काले वद प्रभो ॥ 7.1.18
Here this Chandra (Moon) is on your head. Of whom is he born and how? At what time? Do tell me, O Lord!
Then Lord Shiva describes why Moon is placed on his head:
॥ ईश्वर उवाच ॥ ॥
अस्मिन्काले महादेवि वाराह इति विश्रुते ॥
परार्द्धे तु द्वितीयेऽस्मिन्वर्तमाने तु वेधसः ॥ ११ ॥
द्वितीयमासस्यादौ तु प्रतिपद्या प्रकीर्तिता ॥
वाराहेणोद्धृता तस्यां तथा चादौ धरा प्रिये ॥
तेन वाराहकल्पेति नाम जातं धरातले ॥ १२ ॥
तस्मिन्कल्पे महादेवि गते संध्यांशके प्रिये ॥
प्रथमस्य मनोश्चादौ देवि स्वायंभुवस्य हि ॥ १३ ॥
क्षीरोदे मथ्यमाने तु दैवतैर्दानवैरपि ॥
रत्नानि जज्ञिरे तत्र चतुर्द्दशमितानि वै ॥ १४ ॥
तेषां मध्ये महातेजाश्चंद्रमास्तत्त्वसंभव ॥
सोऽयं मया धृतो देवि अद्यापि शिरसि प्रिये ॥ १५ ॥
विषे पीते महादेवि प्रभासस्थस्य मे सदा ॥
भूषणं मुक्तये देवैर्मम चंद्रः कृतः पुरा ॥ १६ ॥
शशिनाभूषितो यस्मात्तेनाहं शशिभूषणः॥
तत्र स्थाने स्थितोऽद्यापि स्वयंभूर्लिंगमूर्त्तिमान्॥१७॥
This is the period (Kalpa) well-known as Varaha. The second Parardha of Brahma is current now. At the beginning of the second month, this is the Pratipada (first lunar day). Lord Varaha redeemed and lifted up Dhara (the Earth) on this day, O my beloved. Therefore, this Kalpa came to be known by the name Varaha Kalpa on the Earth. In that Kalpa, O great goddess, O my beloved, the Sandhyamsa (twilight period i.e. interregnum of two Kalpas) has passed. The first Manu Svayambhuva was reigning, O goddess.The Ocean of Milk was being churned by Devas and Danavas. Gems, fourteen in number, were born (recovered) therefrom. Among them the highly refulgent Chandra (Moon) is one born of the Tattva (eternal principles). O goddess, O my beloved, he was held and kept on the head by me where he still continues to be. O great goddess, when the poison (Halahala) was swallowed by me while I was stationed in Prabhasa, Chandra was formerly made my ornament for the relief. Since I have been adorned with the Moon (Shasi), I came to be known as Shashibhusana (Moon-ornamented). Even today I am stationed in that holy spot in the form of Svayambhulinga.
So, During the Samundra Manthana when Chandra (Moon) arose from the sea. Lord Shiva used that as an ornament on his head. It also provided relief to Lord Mahadeva from the effect of poison (due to cooling nature of Chandra tatwa).
Moon also exudes Amrita (immortal nectar) on the head of Mahadeva and bathes Mahadeva with it. The heat produced by Vasuki causes the Moon to exude Amrita from it. Padma Purana describes one such incident:
एवं वदति संप्राप्तौ सुतौ स्कंदविनायकौ || २६ ||
तस्मिन्काले देवदेवो यतवागंगमर्दनम् |
चकार च करैर्व्यस्तैर्वासुकिर्भूतलेऽपतत् || २७ ||
हेरंबवाहनस्याखोः पुच्छं ग्रस्तमथाहिना |
स्वपत्रं ग्रस्तमालोक्य मुंचमुंचेत्युवाच ह || २८ ||
अत्रांतरे स्कंदवाहं क्षुब्धं वीक्ष्य महास्वरम् |
तद्भयाद्वासुकिर्ग्रस्तमाखुपुच्छमथोद्गिरत् || २९ ||
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)
When he was speaking like this, the two sons of Shiva, Kartikeya and Gajanana came there. At that time, the god of gods was massaging his body with his hands. Due to his hands being tossed about, Vasuki fell on the ground. Then the serpent Vasuki seized the tail of the mouse, the vehicle of Gajanana (Ganesha). Seeing his vehicle seized, he said: "Leave it, leave it." In the meanwhile, seeing the agitated vehicle, of a large note, of Skanda, 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.
Thus as clear from the verses above Moon also bathes Lord Shiva with Amrita.
The waxing and waning of moon was used to calculate the days and months in earlier times. Thus, the moon symbolizes time and Lord Shiva wearing moon on his head denotes that Shiva has complete control over time and is beyond the measure of time and is eternal. There is also an interesting incident behind the waxing and waning of moon.
Chandra was once cursed by Ganesha to lose his light gradually. And the curse was reduced, upon Chandra's prayer, and he was made to wax and wane, each phase lasting for 14 days (Refer this answer).
Soma is the celestial Moon described in Atharva Veda 11.6.9 which says:
“Soma; whom the learned men call Chandrama the Moon making all delight”.
Atharva Veda Chapter 10 specifies that:
“The Supreme Being keeps making Soma, the eternal delight”
This is empirical to the expression of amṛta dripping from the crescent moon on Śiva’s head in the later Puranas, but before we make this conclusion let’s explore further. Sometimes, Soma is the full moon belonging to the Tiṣya/Pusya month, on this day oblations are given to Rudra. Monday is called Somavara and is the day of Śiva TS2.2.10. Similar to Rudra, the concept of Soma enters into various aspects of the Yajñá (Yagna). In this way, Soma enters into the offering of the Soma juice, into clarified butter called ghee used in Yagna, or the full moon, into medicines, into amṛta, and is the very ṛta. In other places, Somapavamana, meaning the purified/clarified/refined version of Soma, gave rise to both Indra and Viṣṇu during Yajñá RV9.96.5. Now if we move to Baskala Shaka of RV. then ‘ Since the moon is Rudra, so you are Rudra, thereby Rudra harms him not, nor children, nor cattle, .." So, if we keep this link open and continue in later Vedas we can see "Shatapatha Brahamana 6.3 in the origin of Gayatri and Rudra:
"Prajapathi: my son you are the Great God (Mahadeva) I give you that title (Rudra), the moon became him, for the moon is Prajapati, and Prajapati is Mahadeva"
So even before the Puranic literature came to be, Somashekara is a well-established iconification.