Gun is so rare that as a Norwegian I still had to look it up to see if anyone actually used it. Apparently there are about 350 of them vs. about 9000 with "Gunn".

We do have lots of unusual variations in use, though, so I'm not surprised. It was only after World War II that these things were accurately recorded, and so I have an uncle that has one spelling of his name on his birth certificate, one in his passport, but uses a third spelling for everything else. How he's managed to keep that going, I don't know, since e.g. bank records in Norway are keyed to the same central government register used to issue passports.