I've heard several different reasonings over the years. I don't think it actual got him out of a contract but it allowed him to screw the record company. His new 'name' was difficult to market and they had the rights to the 'Prince' name, not his new one, so any new merchandise they created would not be matching the name he was now marketing himself under. Fans are going to listen to him and not the record company. So all in all he was just screwing them out of money and making their job difficult but it didn't actually end any contract.

svantana: for the purpose of Warner enforcing its contract with Prince, he legally changed his stage name, i.e., the name of his act.

Looking at the discography and discussion on the Wikipedia artivle, I don't think the name change got him out of his contract. It seems that he had to release a certain number of albums to finish his contract. I think by using the symbol on those albums, he prevented Warner brothers from having rights to use his name in connection with it. He probably negotiated his next contract a bit differently.

What he did was start turning the crank, churning out five albums in three years, since the contract stipulates a certain number of albums to be produced. Which leads one to wonder if he didn't want the Prince "branding" applied to this work; maybe he thought the label was meddling too much and it wasn't really his work?