Putting the parent's house in the child's name is often a bad idea that will cost you thousands of dollars in additional taxes when you eventually sell the house some day.
You might also be getting yourself into a problematic situation with the mortgage and real estate taxes. The lender is not likely to make a mortgage loan to someone who is not the legal owner. That means that the mortgage will be in your name. Even though you expect your father to make the payments, you will be legally responsible for the mortgage payments and real estate tax. Among other possible issues, if you want to buy a house yourself, the payments on your father's house will be counted as debts that you are responsible for.
Before you do anything, you should review this plan with a lawyer. Whatever the reason is that your father wants to put the house in your name, there may be a better way to accomplish your goal.
