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.)
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