My father would like to put me on the deed to his house. He will still have the mortgage in his name. Just incase anything happens to him. Is there an

If he still has a mortgage, this could cause an acceleration of the mortgage, meaning you have to pay it up immediately.  I don t believe that every happens.  Howwever, there could be other consequences that you should discuss with a lawyer.  Your father could accomplish the same thing by writing a will and leaving you the house in the will.