Your information is interesting. The word in my family when I was a child was that the name Walder/Wallder came from the Black Forest area in Germany where it meant 'forest dweller'. When my cousin was doing National Service in Germany in the 1960s he saw reference of a Walder family crest which was a lion on a shield.
But then I read that the name Walder (from which my name Wallder derives) derived from the WEALD region of Kent and Sussex area in the U.K. When I checked the Registers of Births, Deaths and Marriages from 1837 onwards for the name I couldn't but help noticing that in the 19th century 95% of the British Walders (other than those who had moved to London) came from the counties associated with the Weald ie Kent, Sussex and eastern Hampshire. This seemed to add belief to the Weald theory.
Personally I like the idea of the Walders coming over with William the Conquorer. But of course he conquored the whole of England so coming over with him didn't necessarily mean settling in Kent where he first landed.