Cumberbatch is a modern variant spelling of the ancient surname Comberbach.
Comberbach was inherited from a village called Comberbach. The village is located in Cheshire, England and is a topographical description of the place. The place-name Comberbach means "valley with a stream".
Read about the origin of the surname Cumberbatch.
CUMBERBATCH English: habitation name from Comberbach in north Cheshire, so called from the Old English personal name Cumbra (originally a by name meaning "Cumbrian") or the genitive plural of Cumbre "Britons" plus Old English bæce [meaning] stream. Variants: CumberpatchPatrick Hanks and Flavia Hodges in A Dictionary of Surnames
This may have been influenced by:
'Valley or stream of the Britons', v. Cumbre (gen. pl. Cumbra), bece1, bæce1, but [E Ekwall] observes that the first element could be the OE [Old English] personal name Cumbra ('Welshman'). The village stands in a hollow beside a small brook running into Budworth Mere.E Ekwall in The Concise Oxford Dictionary of English Place-Names, 4th ed., Oxford 1960
This definition would suggest that Comberbach means "Cumbra's stream" or "stream of the Britons". Neither of which I agree with. The definition of the first compound 'Comber' is what I dispute, as this would suggest that Cumberland, Combermere etc were all named after a 'Cumbra'.
However, this same dictionary suggests:
COOMBE English: habitation name from any of various places named with Old English cumb (apparently of Celtic origin) denoting a short, straight valley, or else a topographic name from Middle English combe used independently in the same sense. There are a large number of places in England, mostly spelled Combe, named with this word. The variants in -e for the most part derive from the Old English dative case, those in -(e)s from the genitive. Variants: Co(u)mbe, Coom, Co(o)mb(e)s, Co(o)mber (see also Camber)
So the initial compound of Comber is defined as Comberbach using a historic and perhaps romantic surname origin meaning whilst I believe that it is related to a topographical description of Comber relating to Coombe meaning a valley. See "Coombe Martin" - a valley leading to the sea in North Devon, England.
Cumberbatch Variant Spellings
COMBERBACH - the most ancient form based on the village in Cheshire.
CUMBERBATCH - the modern and most frequently occuring spelling.
CUMBERPATCH - a spelling most often found in the Northampton area of England.
CUMBERBIRCH - another spelling.
Cumberbatch Possible Variant Spellings
Here I should remark that one of my reasons for considering the names Comberbach and Cumberlege identical is the similarity of the arms. John Cumberlege, was a subscriber to Plot's Natural history of Staffordshire, and his arms figure on the folding title to that work, viz. Barry of six ermine and sable, on a canton or a fleur-de-lis gules. The Rev. S. F. Cumberlege, who claims to be of the same family, now bears this coat, and for his crest, a fleur-de-lis between two feathers, with a motto, Vouloir ce que Dieu veut.George William Marshall, in Collections for a Genealogical Account of the Family of Comberbach, 1866
George William Marshall considered the similarity of the arms as sufficient reason to consider the surname spellings as variants and thus to be related to each other. I have my doubts, however the surname origins plotted on a map of England have very high densities which are geographically very close together. Certainly too close to exclude them as possible variants.