Technically ou can say "je m'appelle..." and "je me nomme..." but only the first one is the usual one. But the verb "nommer" as other uses, "nomme-moi" is "name me..." like in the game. (nomme-moi un fruit ! etc.) "Appeller" as oher use too, "j'appelle..." is "I call..." (like on the phone). In these other meaning they are not interchangeable.