How many times has Xavier's School for Gifted Youngsters changed its name in the comics? Have you actually keep some sort of record about it, no matter how hard it is?
About the movieverse, we know that - in the revised timeline - Beast and Cyclops renamed it "JEAN GREY SCHOOL". Surely, in the positive ending of DOFP, the name of the school is STILL supposed to be that one, because I doubt that Xavier would re-rename it after himself, even after Jean has returned on Earth inbetween "Dark Phoenix" and 2023.
Being DEADPOOL an obvious alternate universe, the school is still named "Xavier's School", or so I remember. Is the school ever mentioned by name in any of the DEADPOOL movies?
In LOGAN, another alternate universe, the school is not mentioned at all (if memory serves me well), but they mention the infamous "Westchester Incident".