Volume III, Cham-Creeky
Clarendon Press, Oxford
coomb, combe, comb
[In OE., cumb. masc. 'small valley, hollow' occurs in the charters, in the descriptions of local boundaries in the south of England; also in numerous place-names which still exist, as Batancumb Batcombe, Brancescumb Branscombe, Eastcumb Eastcomb, Sealtcumb Salcombe, Wincelcumb Winchcombe, etc. As a separate word it is not known in ME. literature, but has survived in local use, in which it is quite common in the south of England: see sense b.
1. a. A deep hollow or valley: in OE. charters; not know in ME. but occuring from the 16th c. in the general sense of valley, and more especially of a deep narrow valley, clough, or cleugh.
....b. spec. In the south of England, a hollow or valley on the flank of a hill; esp. one of the characteristic hollows or small valleys closed in at the head, on the sides of and under the chalk downs; also a steep short valley running up from the sea coast.
....c. In the south of Scotland and in the English Lake District, '[in] such hills as are scooped out on one side in form of a crescent, the bosom of the hill, or that portion which lies within the lunated verge, is always denominated the coomb'. (Hogg Queen's Wake 1813 Notes xxiv.)
  Struggling with what the top or head of a valley was called:

I wrote (somewhere) that the head of a valley was the coomb, and I had to look for a confirmation (from mountaineering and geology books as well as from online dictionaries). It seems like my instincts were correct in The Oxford English Dictionary's definition, with section b. being the closest etymological link. But then, I am a) from the south of England, b) quite like old writing, c) have a Middle-English surname and d) used to spend a long time in the mountains.

  Alternatively I was lucky....
  Oh! It seems that Batman's Anglo-Saxon predecessor was Batanmann, and lived in the Batancave. I would imagine that Bruce Waeyne was the scourge of the illegal immigrants from France and Sweden (if they weren't the same thing).