All of the Lennon-McCartney 1968 composition contracts, regardless of who actually composed the song, were signed by John Lennon, alone, on behalf of the Beatles. Paul McCartney's presence and signature were not needed. Neil Aspinall, the Beatles' trusted friend and Apple executive, signed on behalf of Paul and Maclen Music.

Pictured below are scans of the front and back of a publishing agreement for the song,
"Everybody's Got Something To Hide Except Me And My Monkey"
from the White Album. This document was signed by John Lennon October 15th 1968.