A serious portion of the people that are referred to my site are because of this question - I'm assuming for baby naming purposes. I thought I would answer it... although, I do hope you do still browse around.
And, thank you, because answering this required me to do research and I learned more about my name myself. I am extremely grateful to be given the name of such an honored woman with offspring that were so devoted to God, mashaAllah.
So here we go:
Although she is not mentioned by name in Quran, she is referred to, as Hana (i'll spell it this way for consistency) is Imran's wife.
Hana in Quran is more or less the same as Hannah in the Bible.
Being Imran's wife also makes her the mother of Miryam (Mary), and the maternal grandmother of 'Isa (or Jesus).
And, my fellow Hana gets a cameo appearance in just the THIRD surah of Quran:
“When a woman of ‘Imran said, My Lord! Surely I vow to Thee what is in my womb, to be devoted (to thy service); accept therefore from me, surely Thou art the Hearing, the knowing.” (3:35)
Did you miss it? That's Hana, the "woman of Imran."
“So her Lord accepted her with a good acceptance and made her grow up a good growing.” (3:36)
And Hana's prayers were answered as Maryam is one of the four women that is granted the highest levels in Jannah.
So, if you're here because you're looking for a baby name, I would be honored to share my name with your precious child. I pray that she is a blessing for all of the world, and that her offspring too go on to change the world, as happened to Hana in Quran.
I love my name. It's universally wonderful. In English, Arabic, Czech, Japanese, Hawaiian, it has beautiful meanings in every language. It is related to Islam, Christianity and Judaism. It means "bliss."
Congratulations for this blessing Allah is giving to you. May she be devoted to Him, independent of her name.