If a duly authorized peace officer requests it you have to show it.
The law says you must identify yourself if an Officer (not Security Guard) asks you. That means verbally provide name and address. This applies anywhere, operating a vehicle, riding a bike, walking, sitting on a park bench, whatever. If you are operating a motor vehicle w/o having a drivers license on your person, you may or may not get a ticket, at the Officer's discretion.
"Officer, I must have left it in my other coat at home, I'm happy to identify myself to you. My name is (give your real name and address)"., If you are the registered owner of the plates and vehicle, Let him know "I'm the registered owner of the vehicle and/or plates". Or, "I'm the son/daughter of the registered Owner". He probably already ran the plates before he walked up to your car.
Not the OP's question, but something that people sometimes forget.