I check a person's ID all of the time when they're using a credit card. This is to protect the person from someone stealing. So, if you came in with your card with your legal name on it, I would card you and be OK if you showed me the ID that matches the card. If you handed me a credit card that had the name you want to go by on, I would card you but I would deny the usage of the card because the name on your ID would not match that have the card.
It doesn't matter if the chosen name is an authorized user. If it is not on the card and you do not have ID to match it, I would deny usage of that card. This is because of the fraud that abounds, especially since a lot of cashiers, waiters, etc. don't check ID.
If you were using a debit card and used it as debit, I wouldn't care because you need the PIN to use a debit card (unless you're using it as a credit and then I would card you).
You may run into that problem down the road. Someone may want to see the ID that goes with the card and if you do not have a legal document (usually a driver's license, state issued license, military license, passport, or legal resident license) that has the name and your picture, then you may be denied usage of that card so you would have to show your legal documents anyway.
Edit:
@ Paul: I have annoyed people by asking for their ID and always get the line of, "Well, no one else asks for it!", but I don't give a rat's bum. It is fairly easy to get a card in someone's name and then use that card all of the time without getting caught for a long while because people aren't checking the ID. I'd rather have an annoyed customer than have a customer call up where I work and say someone used their card without knowing. I would get in trouble, along with possibly getting fired, and then the company would get in trouble. This goes for just about any company, honestly, but most people just don't check even though they're told that they need to check the ID.
It is for the good of the customer -- to keep someone from using their money.
(If that sounds harsh at all, I'm sorry. I just really dislike the lax attitude towards checking ID, even to the point of asking the cashier if they want to see my ID if I'm running a card as credit.)