Per Olof's birth record has his name as Per Erik. He was born on the 18th of November 1843 in Stigsjö parish:
https://sok.riksarkivet.se/bildvisning/C0033529_00065
But if we look at the husförhörslängd, his name is consistently given as Per Olof from his birth until he moves to America:
https://sok.riksarkivet.se/bildvisning/C0033519_00145
https://sok.riksarkivet.se/bildvisning/C0033520_00210
https://sok.riksarkivet.se/bildvisning/C0033521_00231
https://sok.riksarkivet.se/bildvisning/C0033522_00218