The phrase 'school's name' is correct and usable in written English in certain contexts.
For example, you could use it in the sentence: "Have you heard of my old school's name?".
In 1972 the cadet corps was disbanded, and the school's name was changed to Widener College.
The school's name was then changed to the Agricultural and Mechanical College of Alabama.
In 1870 the school's name was changed to Louisiana State University.
The school's name was changed to the University of Pittsburgh in 1908.
In 1960 the school's name was changed to New Mexico State University.
But when the school's name was called, Rodriguez pounded on the doors of his teammates.
(The AMP in the school's name stands for "Always Mentally Prepared").
Their discussion seemed lively, as they debated the pros and cons of changing the school's name.
The school's name recalls the Arab conquest of Spain in the seventh century.
This is what people would think of whenever they heard the school's name.
Or wanted to change the school's name because "oriental" for some is Eurocentric and offensive?
