My 2 cents
In EVERY military, a soldier will be issued different sets of gear (as all my military brothers can vouch). ie. Standard duty uniform, Desert/hot weather gear, cold weather gear, Dress uniform, blah blah blah.
So if the 501st (or any legion, squad, etc.) has a standard set of "Duty uniforms", it would be the stormtrooper rig (IF they were stormtroopers). If they are deployed for a tour on hoth, then they would be wearing their cold weather gear. A space walk would require a different rig and so on and so forth. So in this case the "TK-xxx" designation would follow a trooper with whatever set of gear he was wearing.
Make sense???