In most of the families that I know the kid comes up with something on his or her own. For example, my cousin's kid uses "mom" when he wants either one of them, and "big mommy" or "little mommy" when he wants one or the other. He came up with these names based on their cars. "Big mommy" drives an SUV and "little mommy" drives a compact car. It's just his thing. He loves cars. And his moms!
If it's necessary for you to know who is who, ask. Otherwise, I think it's safe to assume they've figured it out themselves.