Local authorities refused the mother's request on the grounds that the boy might be teased in later life.
Sara Leisten decided to call her baby Staalman, which translates as Superman, after he was born with an arm pointing up - like the superhero in flight.
The authorities have allowed other unusual names to get through and there are now calls to review the rules.
Tarzan and Batman are allowed, but Superman and Asterix are not acceptable.
A group of MPs are campaigning to get the issue sorted out, saying the current rules are "difficult to understand".
Superman's mum is refusing to give up, saying she may now try to get a similar name - Staalmannen - approved.