English and German from Greek "Dorian woman", i.e. "a woman from Doros", a district in central Greece.  It was the name of an ancient Greek sea nymph [Chambers].

One correspondent [DG] has sent the following note:

"... over the years I have been known as 'Dodie'; 'Dot'; 'Do-do'; 'Doe'; 'Dee' and one especially creative effort of 'Doorknob'...which was meant kindly."

See also Dorian.