By oral family tradition, that's what happened in my family when my great great (great?) grandfather came over from Ireland. The family name then was one of the MacKenzie variations and, I guess, because of his accent, the reception clerk couldn't understand the name, but he did understand "Costley" ... actually, the name of the town that he was from "Castleigh".
Anyway, now we're Costleys instead of MacKenzies.
Some days, it goes like that. In researching my family, I found quite a few name anomalies from one generation to the next, when spelling or pronunciations changed with the fashions.
I find it interesting and really love to dig into other family histories.