Keith,
It is not the sword that has the title but the smith. It is like a family name, helping to identify the person.
Do not worry too much about what is written on the NAKAGO, there is always a chance it is a fake signature, and you cannot be sure unless some real connoisseur or a SHINSA panel has held the blade in hands. But even if the signature was just a phantasy name, it may be a nice sword when restored.
are you saying the signature could be a gemei