Harold Zoid is his uncle. Although he could have dropped the 'berg' and used Zoid as his stage name.
That is a good point, do each of the generations add another ending to the family name "Zoid" e.g. Zoidberg, Zoidfarb, Zoid_ _ _ _ or did Zoidfarb's parents go by the name _ _ _ Zoidfarb? Also was Zoidfarb Zoidberg's cousin's First name or surname?
I was thinking that Zoidberg could be both Clan and Family name. John, of the family Berg, of the Clan Zoid. That would account for why his cousin's name is slightly different - They'd still be related and hence cousins, but have slightly different names.
(or maybe I've read too much Alan Dean Foster...)
As far as 'Norm, Sam AND Sadie', perhaps he was raised by Norm, since Sam and Sadie would have died conceiving him.