As @canadianer mentions in his comment, Protein G is more than likely named after the human group G strain of Streptococci, G148.
Protein G, a bacterial cell wall protein with affinity for immunoglobulin G (IgG), has been isolated from a human group G streptococcal strain (G148).
Purification and some properties of streptococcal protein G, a novel IgG-binding reagent. - Björck et.al.
Protein G is a Streptococcus protein that can bind the the Fc portion of the Immunoglobulin G protein. While it is similar to protein A, it was found to have better binding affinities to the different varieties of heavy chain constant regions of IgG molecules.
The G comes from Lancefield grouping. Lancefield grouping was a method that used to be used to classify bacterium. Group G Streptococci could be identified using Lancefield serum type G and that is how they received their classification.