Sabby is frequently a contraction of either the names Sebastian or Sabrina. I most frequently find it used as a contraction of Sabrina.

My handle was taken from Sebastian Trump which was a wonderful story, so I have less rights to the name than the multitude of people who use it as detailed above. My real name is Daniel.

Sabby is occasionally used as a familiar nickname of the band Black Sabbath, but that's just odd in my opinion... and relatively rare.