Sorry about the EXTREMELY late reply! I've been busy with other things and haven't had the chance to check itch in a while!
How the upgrade progression works is that the next upgrade is unlocked after the previous one was purchased for the first time. The name tag says it does nothing because it doesn't have an actual effect (it's just cosmetic), but since it's an upgrade, it unlocks the next upgrade.
Sorry if my explanation is a bit incoherent. Looking back on it, the name tag's description is definitely misleading!