It seems that Wittgenstein is putting naming before us for a reason: One of the more difficult habits to break is the idea that those language-games that unite words to objects are somehow more important that other language-games, or that they perform a steering role for all of language. By putting naming in its place, we are encouraging ourselves to look at language as a complex adaptive system that has no telos. There are various functions fulfilled, to be sure, but language is not moving toward some goal of perfect word to object symmetry. Your idea that naming is a game that "interpenetrates" many games is suggestive. I'm thinking now that perhaps that simile of language as a mosaic can hold only if we drop the idea that it is composed of rigid tiles with clear and regular boundaries. Naming would be different from one language-game to the next. Natural science as a language game would name things found in the world and then offer a taxonomy. Politics, by contrast, names conventions. These might change more readily than the things named by natural science (though things named by natural science certainly have changed over time). Are we to see these games as having different relations to reality or different realities?
Christopher Robinson & Joseph Duemer read Wittgenstein's Philosophical Investigations