uniquely identify a symmetric key
Any unique identifier would do the trick, including using a hash of the key (assuming you are using a good hash function). Personally I would not use a hash of the key though as it makes an offline attack theoretically possible. If the ID has nothing to do with the key, however, and an attacker steals the ID, there is no advantage gained by the adversary. A simple counter would do the trick. If you indeed need the ID to be globally unique though, simply having everyone generate a random 128 bit number would also work.