Inscriptions for leaders, such as Peking University, are written by Chairman Mao. This usually represents the importance that leaders attach to the school.
Some are collections of words by cultural celebrities, such as Xiamen University, which is the collection of words by Mr. Lu Xun.
And the name of the school inscribed by the calligrapher. For example, Pengcheng University is the inscription of Mr. Li Keran, a famous local calligrapher in Xuzhou.
There are also many schools that are simplified characters, using Song fonts and standard fonts as school names.