If you still have access to your old Xbox 360 console, go offline. Your console caches recent players. Plug in the Ethernet cable after booting up to prevent the cache from refreshing.
When a stranger performs a Gamertag lookup, they will see only your Gamertag and gamerpic. No gamescore, no achievements, no activity. You become a ghost. xbox gamertag lookup
If you’re looking for a new tag and want to see if it’s taken, don't just guess. If you still have access to your old