I would avoid any girls with multiple names
She hasn't got multiple names. she just used different ones at different agencies, loads of them do it for quite innocent reasons. Granted some do to hide a dodgy past, but it could equally be that her name was already in use. I wouldn't discount one on that basis alone, standard due diligence should bring up anything untoward.
Edit
The fact she's willingly stating her past names would make me think she has nothing to hide.