I was dating a guy for 2 years and thought we were going to eventually marry. We ended up purchasing a home together and a year later he ended it. The house is for sale, and he is living there . I want to list it with a realestate agent but he does not want to . I asked him to finance the house under his own name since he still is living in the house and he does not want to do that either. What are my rights to get my name off the mortgage

You get your name off the mortgage note when it's paid off.

Do that with cash or by re-financing.

If your ex doesn't want to do that, you sue him for partition. What you will ask the court is that the house be sold, the mortgage be paid off with the proceeds, and that the proceeds be divided between the two of you equitablly.

Either that, or you file for bankruptcy protection.