Pretender
Sometimes people call such a person a "claimant". The person may be an imposter (someone who is pretending to be someone else).  Often they are pretending to be a prince or other royal person who is missing or whom people think is dead.  However, they may have a genuine right to the throne.  The word pretend comes from the French word prétendre (from the Latin praetendo lit. "to stretch out before").  It means: to profess, to make a loud statement.  In modern English the word pretend  means "to claim falsely".