Please don't read any significance into spelling. 'Correct' spelling is a relatively recent concept, dating from the end of the 19th century. Some clerks would write Crum, and others would write Crumm.
G F Black's The Surnames of Scotland says that Crum and Crumb, derived from Macilchrum, were common in Dumbarton in the 17th and 18th centuries, and that Crumme or Crummy may have been from lands belonging to the Abbey of Culross.
He also refers to Crom, Crome, Cromy, Crum, Cromb and Croume, mostly in Aberdeenshire, and to Crombie, from the place in the parish of Auchterless.
John Milne's Celtic Place Names of Aberdeenshire says that Crombie is derived from Gaelic crom meaning bent or crooked, but he does not say anything about the suffix -bie.
Black also says that MacIlchrum is from Mac Gille chruim (this is unidiomatic in Gaelic and should read Mac a'ghille chruim) which means 'son of the bent lad'. There was a family of Macdonalds who were in Benderloch for 300 years known as Clann-a-Chruim, but he does not cite any references to the name without the M(a)c- prefix.
There is no shortage of place names containing the Gaelic element crom, so there is no need to look to Saxony for its origin.
In my tree I have a John Crum married to Marion Meiklan Waddell. Two of their sons married daughters of Campbell Paterson, who invented Camp Coffee. Also an Erskine Crum who married a relative of mine.
