They were Good Old Games for about 4 years until 2012, when they started selling modern games and rebranded to just GOG, dropping the whole “old games” moniker.
(Yeah, I’m also old. I was there when they rebranded, but I thought it was recently, around 2020!)
Yes, but no. That’s the whole point of the rebranding. You will not find the words “Good Old Games” anywhere in their official materials when referring to themselves. They are now “just” GOG.
They still use “good old game” as a tag for some of the games they sell. But they will never utter those words when referring to themselves in any capacity.
Is it silly? Maybe. But it’s a valid marketing strategy. How effective is it? I don’t know. Maybe ask BP.