These are the notes for GoZync 3. Docs for the latest version of GoZync--GoZync 4--can be found here. GoZync 4 is a free upgrade and is highly recommended (hint: it's faster).
You can rename any of the hosted files, provided you keep your External Data Sources up to date as you would when renaming any FileMaker solution. You'll likely need to rename these if you host your files with a shared hosting provider.
And you can rename your mobile files, of course, provided you keep the External Data Source references in GoZyncMobile up to date.
You can't rename GoZyncMobile, however.