Sorry meant to respond to this. Literally it means “friendly society” (“society of friends”). It harkens back to the Greek independence movement in the early 1800s – there was a secret society that met in Constantinople with the goal of revolution against the Ottoman Turks (Greece had been occupied by the Ottoman empire for 400 years).
So assuming the OS is most directly expressed in the plans of the Society of Friends ( Petros, Elias et. al.), I would say it’s “asserting our dignity” or “showing that we’re still here and that you must reckon with us.”
More broadly, the longstanding goal of Greeks in Cyprus (outside of the novel) is “recover our lost lands and heritage.” That’s kind of assumed in the book, though its not like they have any illusions that putting up a flag would convince Turkey to give back northern Cyprus.
I think that the Friendly Society’s (poorly articulated) goal could be approximated as “finally taking care of unfinished business” – or “shaking loose the frozen situation that was established in 1974” or “forcing the politicians and the world to do something” or even “forcing a change to the intolerable status quo.”
This is seen from the very beginning when Petros is dwelling on the absurdity of a soldier dying on the Green Line – nothing is changed, his death might as well have had no meaning.
They do send their army into the Varosha but it doesn’t trigger another invasion. At the end of the book the government manages to paper over everything so it’s as if this thing (that in reality would have been an international incident) didn’t happen.