Well, it's written in English instead of Aurabesh, so I would assume it was put there by someone from the costume department and not an "in-universe" thing at all. During the period when ESB was filmed, they probably had a lot of costume parts laying around and didn't want to get them mixed up. Hence the logical solution of marking the character's name on the wardrobe.
NOTE: The above was written as an impersonation of someone with no sense of humor.