I'm suprised they didn't turn off their transponder lol.
If you did it, own up. You will learn a great deal of knowledge from ATC - because clearly they dont know how the system works. It's not hard for the controllers to pick up their phone and call the local GAAP airport to get a rego.
I guess if you really stuffed up, and you want to hide it, just use your nemesis rego when you call inbound to the GAAP LOL!