There are costume designators and your Legion ID. Your Legion ID is sometimes called a TKID, even if someone does not have a TK costume. That number is yours for life. Mine is 8020.
Then there are costume designations. TK = stormtroopers, TD = sandtroopers, etc. You get a designator based on your costume, and can have multiple. Most folks do indeed have more than one costume. Thus, I'm TK/TD-8020. By the end of this year I hope to be ID/IC/IN/TK/TD-8020
Usually your acceptance is just a few days turn-around. Unless your GML is on vacation there's no reason for it to take > 1 week.