If your ancestor immigrated to the US before the early 1900s, it's unlikely that there was any one single event (like one 'mistake' by some official) that changed the spelling of their last name forever. There are plenty of cases where older census, county, or even naturalization records have a unique spelling of a last name and it didn't "stick". My own Vance ancestors were Irish but were "Vance" or "Vans" in various censuses and even had both spellings used in the same land deed. Church records were usually more consistent but not always.

You're right that in most cases the family themselves allowed their name to change...unfortunately there was no requirement that they document that, so unless they noted a reason in a bible or family papers, there would be no record of why.

I'm not an expert on the Vances of Wentz origin, but I know some Wentz original immigrants used "Vance" fairly early, like Nicholas Wentz/Vance of Reading Twp, PA, or Handel Vance (Johann Diel Wentz). In some cases immigrants were giving up their past in favor of their new adopted country, so a change in name could reflect a new start or trying to make their children fit in better (like even today when sometimes first generation immigrants don't want to teach their first language to their children).

Or it could be as simple as that there were few German-speaking people in their new community and they adopted the spelling that was easier for everyone else to use (as others have noted, in German "Wentz" would be pronounced "Ventz" so "Vance" is not a stretch. It wasn't the only choice though - I know of at least one line where "Wentz" became "Wence".).

In other cases the original immigrant kept the "Wentz" spelling but one or more of their children adopted "Vance"... in that case perhaps the children just used a form they saw written once or twice, didn't feel a connection to the German spelling, or had their own reasons for the change.

I'm not suggesting those were your own ancestors' reasons; I'm just saying spelling was allowed to be highly variable and which spelling your ancestors finally stuck with had more to do with their own motivations and literacy level over several generations, and what communities they lived in, not what some official might have jotted down once or even twice. Unfortunately that's kind of like asking why they moved to Va... there's no obvious place they would have been likely to write those reasons down, except in personal papers if you're lucky enough to come across those.

Dave Vance