A good portion of the production crew on the movie were from the Philippines, and apparently 'P. Sherman' sounds like the word 'fisherman' spoken with a Filipino accent.
There is another fun Filipino easter egg in the movie, though! Apparently, Nemo's temporary home in the dentist's fish tank is a nipa hut, or bahay kubo - a type of house indigenous to the Philippines!
(Sources: 1, 2)