No, WWE has that name copyrighted, and as such, they get a portion of every movie "The Rock" does. Vince also gets an executive producer credit and the cash that comes with it. I think when Rock leaves WWE, he can opt to buy the copyright, but I'm not sure.
Ahh, I remember reading that the Rock got full rights to his name. And I believe it was Meltz who said it.
EDIT: Well the Rock is in "Be Cool," and is credited as the Rock. Vince isn't credited as an Executive Producer, so me thinks that the Rock does have rights to his name.