The djinn's name comes from
"The Story of Prince Ahmed and the Fairy Panibanou."Â He's correct in that not many seem to have names, based off the research we did.
And, no, the djinn is not a woman as in the fairy tale. The djinn is androgynous.
Edit: Made a slight fix. The name in the comic is Panibanou like in the story. Sorry about that!