Could be that web site B "borrowed" her image from web site "A" for their own use.  Maybe it's part of the old bait and switch game.  It's happened before.  Ask her about it.

Marketing, Brand Identity, etc. Or Stalkers?  EOM

If she uses a different name for each site she advertises on, she would know what sites work for her and what doesn't, based on what name the clients  used when they called. Lots of other possibilities though. I usually see the same person using different names as somewhat negative.

There is a difference.

Actively using two diffrerent names seems a bit deceptive to me.  More than likely it has something to do with stock photos and/or an agency scam, but not absolutely.

I know several very reputable escorts who have changed their names for one reason or another.  A couple of girls that I know did it when they broke their oppression and became true independents.  Callista changed her name becuase people were giving her a hard time about "Sassy".  Another lady I know changed her name and appearance because she came to Vegas to hide from her psycho ex.