Yes it is a small error and a pain in the butt. However, until the error is corrected, the person described as being the licence holder is not you!
Sounds like an overly harsh view.
I bought a house, and the details that came back from the land registry had a similar unimportant administrative error. Nobody threw my tenants out of the house whilst they were fixing it, and a property transaction is (legally) much more of a big deal than a pilot's licence!