I guess I don't really understand this at least with respect to bothering to change the name. I'd try to draw a parallel to what Google did in becoming Alphabet but that doesn't seem to be a congruent situation. The organization of the company around developers as core users makes sense. Not sure if a name change is supposed to do much for the average developer in caring about their product offerings more or less.
I'm not sure whose is the better approach. I think the name change has a bigger impact on Alphabet (the shareholder shuffle, trying to get greater focus on "side projects" outside of the Google core search products) than it will on Stack Overflow. Certainly Stack Overflow doesn't seem to be doing it for outside shareholders, it seems like they are simply doing it to help coalesce their own corporate identity and how they talk about it amongst themselves. It might not directly impact the average developer in caring about their product offerings, but maybe it will help lead communications internally for them in making those product offerings better and selling those product offerings to themselves as important/core to their future. I certainly wish them luck in that case that the name change will indeed benefit their cultural stability and future.