I've showed my Nokia 5110 with prepaid couple of times when checked at border. Usually the first question they come up with is: "Is this really the primary phone you're using." Just smile and say yes. I don't have any other phones with me. That's all I need to contact someone to pick me up.
If you need new identity & SIM card, you can just pick one using cash from SIM card vending machine. Someone said that getting anonymous phone is hard, lol.