If a husband dies without a Will and he is the only name on the mortgage, how does the widow transfer the house into her name?

I can not tell if you are planning ahead but I think that your husband has already passed, is that correct?  I am sorry for your loss.  When some one dies with out a Will it is said that they have died "intestate" and the intestacy laws in the state will guide the personal representative in how the assets are to be distributed. Here, you mention a mortgage but you do not mention the title of the house (in whose name the deed is written).  It is the deed to the house that matters here.  If the house is held jointly with rights of survivorship then it passes automatically to the spouse at the time of death.  If not, then it is part of his estate and will be divided according to the intestacy laws.  The debts that are his are the debts of the estate.  And if the mortgage is in his name alsone then I am surprised that the lender has not requested that it be paid off (but if you were paying it then maybe they did not realize it).   A probate (called an Administration in New York) will have to be done by filing a petition in Probate Court, by appointing a personal representative and figuring out what is what.  The deed can not be transferred with out doing this.  I thnk you need help here.  Good luck.