I heard several times Uma, Laxmi, Parvati. I also heard some story about who was Sati & who is parvati.
Is Uma another wife of Shiva or just a named of Parvati or name of Shakti like Durga/Kali/Bhavani.
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Uma is another name of Parvati as I discuss here. In Valmiki Ramayana:
तस्याम् गंग इयम् अभवत् ज्येष्ठा हिमवतः सुता |
उमा नाम द्वितीया अभूत् कन्या तस्य एव राघव || १-३५-१६
"From Mena, this Ganga is emerged as an elder daughter to Himavanta, and a second daughter, by her name she is Uma, is also begotten by Himavanta, oh, Raghava... [1-35-16]
उग्रेण तपसा युक्ताम् ददौ शैलवरः सुताम् |
रुद्राय अप्रतिरूपाय उमाम् लोक नमस्कृताम् || १-३५-२१
"And that Uma who is unified with her rigorous sacrament thus became a reverential to all the worlds, and that best one among mountains, Himavanta, gave such a daughter to Rudra, an unequalled one in His aspect... [1-35-21]
Similarly not only Parvati, Mula Shakti of Shiva/Maheswara is also called Uma as I discuss here.
Uma is name of parvati mata,parvati mata is daughter of the Himalayas.In Ramayana parvati mata is called daughter of himalayas by the name Uma and Shiva s consort that is parvati mata is usually called by the name Uma.
तस्याम् गंग इयम् अभवत् ज्येष्ठा हिमवतः सुता | उमा नाम द्वितीया अभूत् कन्या तस्य एव राघव || १-३५-१६ Meaning From Mena, this Ganga is emerged as an elder daughter to Himavanta, and a second daughter, by her name she is Uma, is also begotten by Himavanta, oh, Raghava... [1-35-16)
here also uma mata is called daughter of himalayas
या च अन्या शैल दुहिता कन्या आसीत् रघुनंदन |उग्रम् सुव्रतम् आस्थाय तपः तेपे तपोधना || १-३५-२० Meaning
The other daughter of Himavanta, oh, Raghu's descendent, that unmarried girl namely Uma, she performed a rigorous sacrament taking hold of a supreme devoutness as her ascesis itself is her wealth. [1-35-20]
Here uma mata or parvati is called consort of Lord shiva.
न लोका धारयिष्यन्ति तव तेजः सुरोत्तम | ब्राह्मेण तपसा युक्तो देव्या सह तपः चर || १-३६-१०त्रैलोक्य हित काम अर्थम् तेजः तेजसि धारय | रक्ष सर्वान् इमान् लोकान् न अलोकम् कर्तुम् अर्हसि || १-३६-११ Meaning
Worlds cannot capably bear your offspring born out of your effulgence, oh, Supreme-God, hence you may practice yogic asceticism along with your consort Goddess Uma in unison with Vedic postulates of Yoga, rather than progeniture, and desiring the welfare of the three worlds you may please retain your refulgent seed within your own radiance, thus protect this universe, since it will not be apt of you to render it devoid worlds with the efflux of the unmanageable potence of yours .' So said gods to Shiva. [1-36-10, 11]
Also in yajur Veda uma is called the consort of shiva
नमस्सोमाय च रुद्राय च । [YajurVeda T.S. 4.5.8] Salutations to him who is with Uma and who removes cry of Samsara (Shiva)
In earlier scriptures parvati mata is called by the name Uma,in the puranas she is mostly called by the name parvati.
Parvati (Sanskrit: पार्वती, IAST: Pārvatī) or Uma (IAST: Umā) is the Hindu goddess of fertility, love and devotion; as well as of divine strength and power. Known by many other names, she is the gentle and nurturing aspect of the Hindu goddess Shakti and one of the central deities of the Goddess-oriented Shakta sect.
Of Goddesses, one stands above all: Parvati. In certain texts she is even called the Goddess of Wealth, Lakshmi, and the Goddess of Learning, Saraswati, in addition to being idolized as the Goddess of power.
The daughter of the snowclad mountains. The consort of Shiva. The one who is incarnation of all energy, she is A Parvati, also called Uma, Gauri, Durga, Kali and so on.
Her name is said to have been given to Her by Her mother, who upon learning of Parvati's plan to practice extreme self-denial, cried out, "U! Ma!" which means "Oh! Don't!" Alternately, Uma is said to mean "Light," or "The Peace of Night." more can be read here