If Eyder is interchangeable with Eider (which I assume it is since you mention the river) then this is what I've found:http://www.etymonline.com/index.php?term=eider
The Danes call the river Ejderen, so changing the j to a y in English makes sense. Old Norse is supposed to be the origin. I'm unsure if eider became duck because of the marshy lands around the Eider River marsh or vice versa.
As to why it would be a last name it could be related to location on the river or an attribute of the duck that someone once shared.
~Infamous? I think I like that. I'll take two orders of infamous, please.http://klundtacularwrites.blogspot.comhttp://projectwritingroom.blogspot.com/