A Song of Ice and Fire
The Thirteenth Lord Commander of the Night's Watch proclaimed her his queen after he named himself king. So, while "Night's Queen" is never a title explicitly given it can be easily inferred that the queen of the "Night's King" would be called that.
The gathering gloom put Bran in mind of another of Old Nan's stories, the tale of Night's King. He had been the thirteenth man to lead the Night's Watch, she said; a warrior who knew no fear. "And that was the fault in him," she would add, "for all men must know fear." A woman was his downfall; a woman glimpsed from atop the Wall, with skin as white as the moon and eyes like blue stars. Fearing nothing, he chased her and caught her and loved her, though her skin was cold as ice, and when he gave his seed to her he gave his soul as well.
He brought her back to the Nightfort and proclaimed her a queen and himself her king, and with strange sorceries he bound his Sworn Brothers to his will. For thirteen years they had ruled, Night's King and his corpse queen, till finally the Stark of Winterfell and Joramun of the wildlings had joined to free the Watch from bondage. After his fall, when it was found he had been sacrificing to the Others, all records of Night's King had been destroyed, his very name forbidden.
A Storm of Swords - Bran IV
So to recap the story that Bran knows from Old Nan...
- Thirteenth Lord Commander of the Night's Watch fell in love with a woman with "skin as cold as ice and blue eyes".
- Brought her back to the Wall where he proclaimed them king and queen.
- Used magic to control the other Brothers until their defeat.
The Maesters have heard and recorded the same story, although they offer some more insight on how the legend may have began.
The oldest of these tales concern the legendary Night's King, the thirteenth Lord Commander of the Night's Watch, who was alleged to have bedded a sorceress pale as a corpse and declared himself a king. For thirteen years the Night's King and his "corpse queen" ruled together, before King of Winter, Brandon the Breaker, (in alliance, it is said, with the King-Beyond-the-Wall, Joramun) brought them down. Thereafter, he obliterated the Night's King's very name from memory.
In the Citadel, the archmaesters largely dismiss these tales—though some allow that there may have been a Lord Commander who attempted to carve out a kingdom for himself in the earliest days of the Watch. Some suggest that perhaps the corpse queen was a woman of the Barrowlands, a daughter of the Barrow King who was then a power in his own right, and oft associated with graves.
The World of Ice and Fire - The Wall and Beyond: The Night’s Watch
So the Maesters may answer your question that the true identity of the "Night's Queen" is that she was just a "Barrowlands Princess".