just reading this and I wonder .... if this is supposed to be a specifically Jewish name, and this can be proven, I'm probably wrong.
However, would I hazard a guess, I would say this name way back may have been the German name Nestelberger instead.
Neftelberger, shown by the ...berger ending actually sounds like a German name. The Austrian phone directory for instance doesn't have a single entry for Neftelberger, but has lots of Nestelberger. Personally I've never heard of a Neftelberger, but of Nestelbergers.
How may this have happened? In old German script there's a 'long s' which is written and sometimes looks nearly like an f. I would guess that maybe in the past people started reading the (long) s as an f and made the name spell Neftelberger ....
But of course, this all may be totally wrong as well ...
Just an idea.