'Beijing' as in 'Beijing University' has special meanings for many, especially old generation of alumni. In CCP China, 'Beijing' represents the one and the only one. For example, some may remember the 'Beijing' TV. Even though it was produced in Tianjin, it was named by late premier Chou as 'Beijing' because it's the first and best in China.

Associating PKU with 'University of Beijing' sounds a downgrading.