The German phone directory lists 7 EUGLINGs, so this is a v e r y rare name.
I can't find the name in any of my books, but there are plenty of names ending with -ing or -ling: Rehling, Kiesling ...
Sometimes the L is part of the (patronymic) suffix, sometimes it isn't. Many of those names go back to a place name, e.g. Rehling (or Rehlingen). No place called Eugling or Euglingen seems to exist in Germany - but it may have existed in the past.
The syllable EUG is not German, it looks Greek to me, probably from the name EUGEN ("well-born").
So I see two possible derivations of EUGLING:
- Son of Eugen
- Someone from Eugling(en), which again derives from Eugen
But maybe it is something completely different ...