The name "Elswick" is first recorded in A.D.1189 as Elstwyc, later (1198) Alsistwic

Ekwall (Dictionary of English Place-names, 1936, 1960) gives the derivation from Old English Ælfsiges wic - 'the farm of Ælfsige'

Ælfsige is an Old English personal name.

wic is the Old English word for a farm. It later appears to refer to farms of a particular type on an estate. It may be that those compounded with personal names refer to earlier settlements, but this is unproven. However, some wics are certainly very early settlements.