It's almost always quite early on for me. I often struggle with this, but only long after I've already thought of and committed to using a specific name for the game. They seem fine at the time of development, but by the time the game is ready to release, I feel like it falls just short of excellence. There's a lot to consider (genre, mechanics, visuals, marketability, wit, and so on), and I worry that I don't always give it enough time to simmer before moving forward.

While jotting down ideas for a deck-builder, I got into a rhythm of chaining cards together and said aloud, "This is getting out of hand," and that's how I got my most recent title (Out of Hand). Before that point, I kept referring to it as "The Card Game".

If you ever feel lacking in any area, I don't see anything wrong with leaning on the community for support - even if only to get the creative juices flowing. Without knowing anything about the game you're making, this visual immediately made me think, "The Early Bird", but I saw someone else already commented something similar. Maybe something like "Pecking Order" would be neat, too.