Stephen F Austin is a very famous person in Texas history. He led some of the first settlers from the US to Texas, that is how his name is spelled. I think the connection may have become just a family tall tail, after the grandfather was named Austin.
I meant farther back in Stephen F Austin’s history, there may be different spellings. We’re talking about a culture that seldom had formal education for the masses.
How many names do you think were re-spelled or re-given during the days of Ellis Island? Often, a name was spelled as it sounded, or if that was an impossible task, a person was renamed for the country or city they came from.