Adelelm is a Continental Germanic masculine name corresponding to Old English Æthelhelm (which comprises the elements æðele ‘noble, famous’ and helm ‘protection, helmet’). As von Feilitzen (1937: 78-9, 184) points out, the insular spelling of Æthelhelm had become reduced to Æthelm (whence DB Ailm) by c.940 and so the Adelelmus and similar forms in DB are probably derived from CG Adelelm not OE Æthelhelm. This interpretation has been adopted here with regard to distinguishing between the two names.
The PASE corpus does not record any pre-Conquest instances of the name but does note Adelelm 1 as the abbot of Abingdon (1071-83).
von Feilitzen 1937: O. von Feilitzen, The Pre-Conquest Personal Names of Domesday Book, Nomina Germanica 3 (Uppsala, 1937)
Spellings in Domesday Book: Adelalmus, Adelalnus, Adeledmus, Adelelmus, Alelmus
Forms in modern scholarship:
von Feilitzen head forms: Adalhelm, Adel(h)elm
Phillimore edition: Aethelhelm (TRE); Adelelm, Adelhelm, Aethelhelm (TRW)
Alecto edition: Æthelhelm (TRE); Adelelm (TRW)