Having your name on the V5 just means you are responsible for keeping it taxed and MOT'd etc, it does NOT make you the legal owner.

So although yes, you can get a V5 for the car in your name, it's still theft to tow it away!

An example of this is I purchased my wife's car, the receipt has my name and signature on it. The V5 is registered in her name. If we were to go our separate ways, I own the car, as I can prove I paid for it, having her name on the V5 means fuck all.