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Realm transfers and name changes are offered as a premium World of Warcraft service, and offer a degree of anonymity. However, this information can often be sleuthed.
When looking at WarcraftRealms' character history data, you can usually tell a character has had their name changed, or were recently transferred to a server, based on their initial time and level seen on the server. If a character suddenly appears at level 80, it's a good clue that they weren't on the realm before hitting 80 - or if they were, it was under another name.
WoWProgress also has a Detective that can help do some of the guesswork. You can search by realm to see what the tool has detected as name changes or transfers, based on character information such as gear, guilds, and achievements. This tool is experimental and often lacks data, but is the only of its kind to offer such information.