Re: William Barnidge b. 1815, Ireland. Immigrant to Louisiana
The P is Alonzo P. is for Pinckney. That may have been his grandmothers maiden name - mother was Eliza Swan, grandmother Rachel (Pinckney) Swan.
So maybe the P was also for Pinckney. Some of these names seem to crop up here and there. I think another relative somewhere back there had the surname of Pinckney which might have been a little hard to live with.