In my personal head-canon the Fat Lady was Godric Gryffindor's sister but she died before the castle was complete and her brother gave her a place guarding his future students.
I really do think they should ask her name or at the very least call her something less offensive like The Pink Lady (doesn't it say she wore a pink dress?)
Gryffindor: the house of bravery and chivalry. And yet not one of them asks my name. They think that just because I'm a portrait I don't have feelings. And so, every year the new prefect gives the first years a speech.
'And this is the Fat Lady'
Don't they know anything about chivalry? – It's things like holding doors open or pulling out chairs and NOT calling women fat.
Just once I wish someone would talk to me; ask me who I am? Why I was placed in such an important place?
My brother would be so ashamed of his students.