Aldithf.Old English(e)ald 'old' + Old Englishgȳð 'war'.
The name does not appear to have survived beyond the 14th C as a personal name, but it appears in the English placenames Audley (Stafs) and Bewaldeth (Cumb).
Cite as: S.L. Uckelman. "Aldith". In S.L. Uckelman, ed. The Dictionary of Medieval Names from European Sources, Edition 2017, no. 1. http://dmnes.org/2017/1/name/Aldith.