Can my new husband leave his home to me in a will even if he would still owe money on it at the time of death. My name is not on the mortgage or deed. And can I do the same for him in my will with my home. His name is not on my mortgage or deed either. The mortgage companies want us to refinance to have both of our names put on the homes. Please help with this. We are both in our fifties and need to write a will. I can't seem to find an answer. Also, what does the mortgage company do concerning changing the name on these homes if one of us would die? Thank you for any help that you can give me on this!!!!