I believe it should still be called Xavier's mansion, and we can assume Xavier came back and stopped with his nonsense retirement. Once Jean came back, she most likely refused to take the name, and granted Charles permission to have the original name. This is because in Deadpool, it was definitely called Xavier's School for Gifted Youngsters, based on the plaque outside.
Honestly, screw the person who came up with the ending. It has so many plot holes. It's as easy as literally watching the movies.