According to Skanda Purana, Volume 15, Chapter 171, her name was Sandili.
According to this chapter, Sage Mandavya was ordered by a King to be impaled though he was not in fault. When Sage Mandavya was in such situation, one night a Brahmani Sandili came there with her husband and by mistake she felt on Sage Mandavya. This caused more pain to the sage and he cursed Sandili that her husband will die at sun rise. In return Sandili cursed him that Sun will not rise. But here, there is no mention of Anasuya rather Sandili was pacified by Devas.
40-44. When those leading Brahmanas went out of sight, the female ascetic Sandili came there on the second day. She was carrying her husband on her head and wandering about at night.
She did not see the sage (Mandavya). O Yudhisthira, she was staggering due to the excess of burden. The Brahmana on the stake was not noticed by her. The chaste lady faltered and slipped down against the knees of the Brahmana on the stake. Due to the fall of the faltering lady much pain was caused to the sage. Along with the previous predicament caused by fate, the present situation became will-nigh intolerable. He said: "A further infliction of the fruit of sin Alas! My pain is great! O sinful lady, I have been further pained by you in a fruitless task. Why? I see you as a wanton woman wandering as you please. Are you a female thief or an ogress?" After saying this and lamenting again and again he fell into a swoon.
45-54. The sages and all the ascetics were agitated in their minds on being aware of the sufferings of the sage (Mandavya). They then asked her, O Yudhisthira:
“Why do you wander about at night. What is it that you are carrying? Something weighty has been put into this sack. What is the purpose of your arrival here? You have caused pain to this sage, O lady, reeling in misery and going through sorrow after sorrow.
Know ye all that I am neither an Asuri nor a Gandharvi, neither a Pisac nor a Raksas. Understand that I am a chaste woman loyal to my husband and steadfast in my penance.
I am not overwhelmed with lust or anger, I have no enmity with anyone, nor am I afflicted by jealousy. I did falter and slip down due to ignorance and due to the fact that my eyes could not see properly. It behoves you to pardon me.
For the comfort of my husband, I carry him, as at day time he is troubled by his ailment. Please know that he who is always in the sack is my husband. I bear him, feed him, dress him as he is a patient. Know that this sage is the leader of Saunaka clan and that I am his wife Sandili. Please do not get angry with a chaste woman serving my husband righteously. Treat (us) as guest. It behoves you all to pardon me who have come near saintly persons like you.
The sages said:
Moving about at will, you appear to be unaware of other people's distress and pain. In the morning as soon as the sun rises your husbad will die. O low-born woman, only your own misery you know and not that of any other person.
Sandili became chagrined at those terrible words. Afflicted with grief, she was lost in meditation for a short while. Then her eyes became red with anger. Staring at the sages she spoke these words:
55-60. "When a good person visits the house, he should be accorded the adoration due to a guest with gentle and welcoming words. It seems, I have come to the house of you good people in the guise of one committing an offence. This is the type of hospitality accorded to me by you all! The righteous conduct conducive to heavenly pleasures and salvation was not at all noticed by you. I am a Prajapatya (the progeny of a patrichal family) but you see me like a barbarous woman. May you and the deities in heaven see women's power in me today. My husband will not die. The sun will not rise. The entire universe will be covered with darkness. The night will not come to an end.”