There is some dispute over the origins of the surname Muschamp.

L G Pine, in his book "They Came With The Conqueror" stated that Roger and Robert Muschamp were both recorded in the Domesday Book and that Roger held Wilgebi. 

I have completed a search of the Domesday Book and can find no trace of the Muschamp surname anywhere in that document! Also, the Lord of Wilgebi is only referred to as "Roger, Gilbert's man"! No surname given!

Unfortunately, L G Pine's book does not list his sources so I am unable to determine where he obtained his information. 

Based on the above, I am leaning towards the possibility that the name came from North and South Muskham! 

Yes, the first of our ancestors to set foot in England may well have been Norman, but I do not believe they were titled at that time, but may have been generously rewarded by Gilbert of Ghent with titles which later led to them having a surname!