I know for Odyssey Yasuo it's "Song" (because it sounded cool, not for any real meaning), and some fan sites speculate that base/canon Yasuo's sword is "Last Breath," but I don't know whether it's been made official.
It seems equally in character for him to name it or not to name it. On the one hand, it fits the cool samurai archetype for him to use "Windpiercer, Daughter of the Seven Fires, Eternal Sword of Heaven"; on the other, he seems pragmatic enough to say "What?! No, it doesn't have a name. It's a sword."