There's a lot of ways. For my own game company, the whole team talked for a while and we tried to come up with... concepts and ideas that brought us together.
We talked about a ton of stuff. The whole team have similar taste in music. We've all played role playing games together (like, D&D style role playing games) and have had an absolute blast with it. We like telling stories, but we also like keeping things somewhat goofy and lighthearted. And definitely, absolutely we're super invested into fantasy worlds. Magic. Fun characters.
We danced around those concepts for a while, and we landed on the concept of the bard. Like the medieval bard. The guy that plays and writes music and tells stories. Also the goofiest D&D class. We envisioned a magical bard traveling through the universe and running into all sorts of fun shaenanigans and weird adventures. Basically thinking about this... almost character, on a conceptual level. Eventually we convined the idea of the Bard, and the Stars (which btw, is also kind-of in honor of our first game's main character, who has a star motif going on and is also named after a real star). And that led to Astrobard Games, which became the final name.
Now, the method is not perfect (I still stumble a bit when someone asks why we're called that, lol), but it's still a method and it worked decently for us. Think about the things you have in common with your team. The things you all stand for. The type of games you want to create. Even just... things you like. Think of a way to put those things together in one concept. Then think of fun ways you can use that concept.
Alternatively, you can just not think too hard about it and pick something that sounds cool. For example Blizzard famously got their name because they literally just decided to find cool-sounding words in the dictionary and got bored when they reached B.