The word "(traded)" after the character's name in a message or post as well as the hint on texts written on items are only displayed for 30 days after the auction ended if the character has not been renamed.
If you want to check if a character has been traded over 30 days ago or in case it has been renamed after being traded, you will have to use unofficial features to look for name changes history, such as TibiaRing, and to search for past auctions, such as NabBot's $auction CharacterName command.