The only significance that Bradbury himself attributed to Faber was in the afterword, where he mentions that "Faber" is also the name of a pencil company:
Only recently, glancing at the novel, I realized that Montag is named after a paper manufacturing company. And Faber, of course, is a maker of pencils! What a sly thing my subconscious was, to name them thus.
(Bradbury, Fahrenheit 451, Google Books)
Bradbury's unspoken interpretation of this is that Faber, the Professor, instructs Montag in various ways. Just as a pencil writes on paper, Faber "writes" his ideas on Montag, who is still a blank; Montag has no concrete idea what to do with his new-found individualism, and Faber helps him to understand it and mold it into something worth preserving. In this sense, Faber is the Knowledge and Montag is the Vessel; the Vessel will remain empty without the Knowledge, and the Knowledge will die if it is not transferred to a new Vessel. Therefore, Bradbury shows how the subconscious often attributes ideas and themes into writing that may not be deliberate.
The only things I could think of is Faber's name starts with f and ends with r just as fear starts with f and ends with r. Faber is fearful of what the society has become, and his name strongly resembles the word fear. (take b out, and switch a and e.)
Faber is also the name of a pencil manufacturer--see Bradbury's "Afterward" from the novel.