I think it's likely to be from the Dutch name Deliana, which crossed the Channel to Norfolk when Dutch engineers and labourers went there to help drain the Fens. Deliana is derived from
Delia in much the same way that
Juliana is derived from
Julia. It is said that the English version is Dillian, which is interesting and rather nice, but I've never met or heard of one in real life. (Or there's always
Dilwen, of course.)