Just to throw out some ideas.
I think in a lot of cases (although not all) nicknames tend to be shorter than the original name. Imagining old school ones like Robert → Bob, or Daniel → Dan etc. It’s hard to shorten OGS to just O or GS or something 
Although in some cases nicknames are a similar number of letters but maybe less formal like Charles->Charlie. Could call OGS->Gus.
Then in other cases nicknames have nothing whatsoever to do with the original name but of some property or trait of the individual or just some story about them (or website in this case). So we should just all call it Nova to confuse people.
Then another option that Gia gave
Some kind of Sports nickname for OGS like “The Best of the West” - as in the best western Go server