A few -ston(e) placenames probably began as Something-stan, meaning stone.
But the majority appear to have begun as Somebody's-tun, meaning farmstead. They acquired an -e in the olde worlde dayes when everyethinge had an e.
Most of those places dropped the e later, but some hung on to it. In those cases, you get both spellings in the 19th century, and the -stone spelling didn't finally win out until the 20th century.
As for the surnames, some people tracked the placename spelling and some people stuck with the older form. Nobody could say which was the right policy. No surname came out of the box with an original permanent spelling. In Britain, locational surnames mostly do tend to track the spelling of the placename (yes I know there are many exceptions).