My mother's mom has been deceased since 1985 and my mother has been paying the mortgage but house is still in her mom's name. How does my mom get house in her name instead?

If the house is solely in your grandmother's name, then your mom will most likely have to go to probate court to get this done. She will need to prove that she inherited the house to get her name on the deed.

The best place to start would be the County Clerk's office. They will explain what she needs to do.

As Scott said, this should have been done back in 85 when you probated your grandmothers estate. But at this point you will have to go back and prove that she was the sole heir, a copy of the will should provide it.

I am surprised the lender has not demanded this to be done before now.

As long as the lender is getting paid, they might not even know that the owner is deceased. This actually happens all the time. As long as the bank is getting their payments on time, they won't question where the payments come from.

I guess they may not, just thinking about my dad's passing, the funeral home like notified everyone for us, took care of all the details.

I wonder while we are thinking, what about the property tax records,
What about the property insurance, if that is not changed, and there was a fire, would they pay if the person insuranced has been dead 20 years.

Yes, leaving the house in the deceased's name is a dangerous thing to do. It could cause all kinds of trouble.