In Valmiki Ramayana, at several places Sita's mother (referred to wife of Seeradhwaja Janaka) is mentioned, but nowhere her name. In any other Purana, name of Sita's mother is mentioned? If so, where and what it is?
According to Tulasidas's Ramacharitamanasa, Balakanda, 1.324, name of the wife of King Janaka was Sunayana.
जनक पाटमहिषी जग जानी। सीय मातु किमि जाइ बखानी।।
सुजसु सुकृत सुख सुदंरताई। सब समेटि बिधि रची बनाई।।
समउ जानि मुनिबरन्ह बोलाई। सुनत सुआसिनि सादर ल्याई।।
जनक बाम दिसि सोह सुनयना। हिमगिरि संग बनि जनु मयना।।
कनक कलस मनि कोपर रूरे। सुचि सुंगध मंगल जल पूरे।।
निज कर मुदित रायँ अरु रानी। धरे राम के आगें आनी।।
पढ़हिं बेद मुनि मंगल बानी। गगन सुमन झरि अवसरु जानी।।
बरु बिलोकि दंपति अनुरागे। पाय पुनीत पखारन लागे।।
What words can describe the world-renowned queen-consort of Janaka and Sita's mother? The Creator had exhausted in fashioning her all the bright glory, virtue, joy and beauty. Perceiving the appropriate time, the great sages sent for her; and in response to their call married women whose hasbands were alive brought her with due honour. Queen Sunayana shone forth to Janaka's left even as Maina beside Himavan (the mountain- king). The king and queen joyfully brought and placed with their own hands gold vases and beautiful trays of jewels filled with holy, scented and auspicious water before Sri Rama. The sages recited the Veda in joyous tones and at the proper time flowers rained down from the heavens. The royal couple were enraptured to behold the Bridegroom and began to wash His holy feet.
BTW, mother Sita is said to be the daughter of mother Earth but technically, Sunayana can be said to be her mother.
Her mother was Yogini as written in Shiva purana.
धन्या प्रिया द्वितीया तु योगिनी जनकस्य च। तस्या कन्या महालक्ष्मीर्नाम्ना सीता भविष्यति।।
- The second daughter Dhanyā shall be the Yoginī, the wife of Janaka. Her daughter shall be Mahālakṣmī in the name of Sītā.