I'm not sure the Aidric in that form goes back to medieval times, but
Aldric or variations of it were certainly in common use in England then. We know that because there are many English surnames based on
Aldric -- Aldrich, Aldrick, Alldred, Alldridge, Allderidge, Elderidge, Eldridge, Eldrick, and Oldridge, according to Reaney &
Wilson's
A Dictionary of English Surnames. All of these surnames would go back to the family having an ancestor named
Aldric or some variation of it in medieval England.