I used to spell it 'GaGa' because I'd seen it used in official media, although it went to and from 'Gaga'. Otherwise I wouldn't have done that. But 'GaGa' is never used in official media today- it's always 'Gaga', so that's what I'm sticking with :)
I´m a webmaster of fansite about Lady Gaga and I remember I used to write "Lady GaGa" because I thought it´s cool :) and some people told me that I´m stupid because she´s "Gaga" not "GaGa" so... :D I prefer Lady Gaga :)