My father has been dead for over thirty years. His name was the only name on the deed to the house. My mother has lived in the house all these years. Is it necessary to change the name on the deed. If she does, what will this do to my half brother's interest when she passes on?

At this point you basically have a legal mess, She would have inherited the house at the fathers death most likely, so even without changing the name on the deed, she has a legal claim to the home.

So if she dies, her heirs can fight in probate court to keep any heir of the father that is not a hier of the mother to stop them from getting anything.

So from a legal standpoint, any heir of the father, not part of the mothers estate most likely will not get anything now if it goes though probate

But the mother should have had it changed years ago. But her right to change it, and her heirs right to ownership is not taken away because she did not.