No Playstation is a Video Game console and the Sony Phone has a different name called Ericsson. They do have a phone Sony Xperia Play and some articles call it a PlayStation Phone. The Xperia Play is a sleek new smartphone plus portable gaming device see related link
I guess you could call it a Playstation phone and it sells for centersooq under $100 with a Verizon contract, but the actual name is Xperia Play and it does have gaming controls similar to the PSP