The name itself comes from a word meaning someone who makes stuff. It comes from the Latin word meaning a craftsman.
In the afterword to one edition of the book, Ray Bradbury points out that Faber is part of the name of a pencil making company, Faber-Castell. But he says that he did not consciously name Faber after the pencil company.
He thinks that maybe unconsciously he did and that he named Montag after a paper company because pencils and paper equal writing equal books.
So it does not seem that Bradbury had anything in mind when he named the character.
Faber is a name of a pencil company