Well, In the Aberystwyth University online dictionary I found a word "mynog" (pronounced muh-nog, with the accent on the muh)which seems to be a rare adjective meaning noble or princely, so Due Mungo could possibly come from a mutated Duw Mynog, which would mean Noble God. Duw is pronounced like the English word "due".
Which could of course be totally inappropriate!
Cheers
Ray