Her whole image is a persona and she is obviously putting on an act in order to not dissapear from the spotlight. I think she wants to keep herself to herself when she is "Lady Gaga" as was shown on Jonathan Ross... she wants to be someone who is secretive (Michael Jackson and Madonna) were the same when being interviewed generally.
The real Lady Gaga (Stefani), there are some pictures:
http://celebrities.ninemsn.com.au/im...0209_gaga2.jpg
http://images2.fanpop.com/images/pho...64-480-359.jpg
the first picture shows how much or a "normal" person she is, that is the real her.
The 2nd picture shows that she can have fun, it would be nice to see this "Lady Gaga".
There also was a picture of her holding a baby, walking down the street, with no outrageous outfit or makeup, and she looks quite naturally nice.