What does this do?
I haven't clicked on it fearing it will automatically change something in our league.

Also is there a way to prohibit GM's from changing player names of non-rookies?

When you create a league, you can customize it each year but you have to use credits. If you want to customize after the first season, you turn on customizations for that season with this option. If you don't intend to do any customizations for the current season, you don't need to use that feature.

After the first season, only rookies are renamable.