Dane is here interesting. Why not Denmarkman or Denman or Danishman? Which one of those is correct in same way?
A Dane, a Swede, a Norwegian (Norseman brings to mind beards and battle-axes), a German, a Welshman, a Luxembourger.
English is weird!
Source: An native English speaker of His Majesty the Kings English, not one of those weird leftpondian dialects :-)
It is usually easy to understand if you just look into it.