Is it OK to rename an application?
Generally, it does not affect, but there are some apps that don't properly work when you do it. 

The only way to know is trying it. In the worst case, you can revert the changes without issues.

About accessing keychain, same thing, usually you won't have problems.

I haven't tested auto-update. I usually did it with old versions of apps, to have both old and new ones.