How did the p site of the ribosome get its name?

The ribossome has three sites:

first: A-site (aminoacyl)

second: P-site (peptidyl)

final: E-site (exit)

While the translation of a protein happens, the P-site holds the t-RNA, which is bonded to the growing polypeptide chain of aminoacids.

That's why it's called a P-site, there is a bind between the peptidyl and tRNA.