Pater is a wel know surname in Europe.
Most in Holland but also in Germany and Poland.
Where the name comes from is not sure.
Mayby the Pater-Familias. We have in Holland also the name Abba (hebrew) Pater (Roman) and Vader (father in Dutch). We know in Holland also the surname Priest, Bishop, etc.
The oldest name Pater in Holland is around 1450 but we found a Pater in Julich in Germany just accros the border with Holland in 1248.
Here in Holland we (the Family Organisation Pater) are the largerst Family Organisation. We have about 30.000 familynames in (for the moment) 7 trees.
Next April 13th, we celebrate our 20the anniversary.http://www.fam-org-pater.nl
(sorry, only in Dutch).