And to add to the Pohl spelling, I give this explanation also.
Most of the written records in Spanish from the 1850s to 1900s spell the name as "Pol". Most of the Federal censuses spell it as "Paul".
If you've ever heard someone who speaks mostly Spanish pronounce the name of Paul, you will understand why it sounds like "Pole" or "Pul". And keep in mind that the Parish priests, who wrote the marriage and birth records in Spanish, were from France, and Spanish was a second language for them.
I've spent 3 years researching here in New Mexico, and am pretty sure, there is good reason anyway, to believe that the original name was Paul.