What does the name Griff mean?

I think it means "rumour" or "information received on the grapevine". It may have originated in the army during or before the Second World War.

A book entitled "Memoirs of An Army Surgeon" was published in 1948 by James A. R. (for some reason the author´s surname appears nowhere in the book! Just the initials J.A.R. on the front cover). I quote from the "Invasion of Sicily" chapter, page 143: ".....several of the crew also came aboard, and the South African medical orderlies crowded round these sailors to get the griff on the invasion."