Derby, in the Morleyston and Litchurch Hundred of Derbyshire, is the the only one of the Five Boroughs of the Danelaw to bear a Scandinavian name. It is also one of the few instances of a Scandinavian-named place for which we have an earlier English name.
The English name is Norðworðig from the Old English elements norð ‘north’ and worðing ‘enclosure’. This is possibly related to Derby’s position, slightly north-east of Tamworth and that the enclosure’s northernness is relative to the ancient capital of Mercia.
In standard reference books the name Derby is explained as Djúrabý, comprising Old Norse djúr ‘deer’ and by ‘farm, settlement’. Furthermore the compound recurs in the British Isles, and probably refers to a particular function- djúrabý ‘specialised production units that had earlier formed parts of multiple estates’.
However, the first element of the name probably has a completely different derivation based on its location on the River Derwent, whose name is pre-English in origin. The form of the river-name in the Anglo-Saxon period was Deorwente. Scandinavian settlers hearing this river-name could have associated the first element deor with the familiar compound djúrabý, or indirectly adapted the Romano-British settlement name Derventio. It is certainly possible that the Romano-British name continued in use to refer to the fortified area in the Anglo-Saxon period.
Mint-signatures from Derby point to the likelihood not only that Deoraby originally referred specifically to the area of the Roman fort, but also that it is a Scandinavianisation of a pre-existing name of British origin used by the Anglo-Saxons.
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Kenneth Cameron, The Place-Names of Derbyshire II. English Place-Name Society Volume XXVII (1950-1), p. 446.
Jayne Carroll and David N. Parsons, Anglo-Saxon Mint-Names: I. Axbridge-Hythe, Richard Coates ed., English Place-Name Society Extra Series Volume 2 (2007), pp. 112-120.