First, when you are referring to an existing entity like a society you should use its exact name. If the society is called "The Gilbert Keith Chesterton Society" then you should call it exactly that. No variants.
When it comes to naming a society, then "The X Society" implies an interest or relationship to X. "The Society of X" implies composition of X.
To take an example "The Society of Painters" would be assumed to have members who were all painters. "The Painters Society" might be composed of painters, but it might also be composed of people who were interested in painters.
"The Society of The Last of the Mohicans" would be assumed to have members who were the last of the Mohicans. "The Last of the Mohicans Society" would be for people who were interested in The Last of the Mohicans.
The "Society of Gilbert Keith Chesterton" or "The Society of the Last Mohican" would have very limited membership indeed. If we are naming a society for people interested in GKC or LoM then use the first form.