Did you say you've tried giving her to others to take care of? How long have she been hanging around?
I think you should name her because pretty soon her REAL name will be Nameless. Or some variation of kitty, sweetie, honey, etc. :D You don't want to be stuck with a nameless cat for the next 15 to 20 years, now do you? ;)
And 3 really isn't that much compared to 2. I whined to go from 2 to 4, and can't remember what life was like as a two kitty family. Three sounds perfectly sane to me!