The Old Norse male personal name Eiláfr/Eileifr is not always to be distinguished from another Old Norse male personal name Eilífr. This is evident in the place-name Elston, Nottinghamshire where the first element is either Eiláfr or perhaps Eilífr. 

Eiláfr/Eileifr is an Old Norse compound name with the first element being either Ei- ‘always’ or Ein- ‘one, alone, single’ combined with the second element -leifr/-láfr ‘inheritance’ which when used in a personal name likely has the sense of ‘son’.

This name was frequently used throughout medieval Scandinavia and is attested in Danish place-names and runic inscription, Swedish runic inscriptions, and became common in Norway after 1270. The name occurs in Domesday Book, and later medieval documents, for both Lincolnshire and Yorkshire.