No it is not Austrian, it is actually a German and Ashkenazic Jewish surname
Brane Gruber's birth name is Gruber, Branko.
Kelly Gruber's birth name is Kelly Wayne Gruber.
Astrid Gruber's birth name is Astrid Cristancho Gruber.
Bruce Gruber's birth name is Bruce Barrett Gruber.
Ruth Gruber's birth name is Ruth Ellen Gruber.
Kelly Gruber's wife's name is Michelle Gruber.
Lilli Gruber's birth name is Dietlinde Gruber.
Father Josef Mohr, an Austrian priest wrote the lyrics.Franz Xavier Gruber composed the melody.
Scarlet Gruber's birth name is Scarlet Alexandra Fernndez Cristancho.
There is no such language as "Austrian" but if you mean German, the name James is spelled "Jakob" in German.
Gregor Mendell was an Austrian Monk, living in a monastary in Austria. He was religious and did his work since he was the gardener of the monastary. Therefore since he was Austrian, the name Mendell is an Austrian name.
Josef Franz Mohr was an Austrian priest who wrote the poem on which the carol "Silent Night" was based. He had struck up an acquaintance with Franz Gruber, who lived in a nearby town, and Gruber offered to write the music for the song. "Silent Night" has been a traditional part of Christmas celebrations ever since.