I wouldn't necessarily make it truenaming (although I like the idea) simply because the idea that beings (all? some? only supernatural ones?) have true names isn't something that's been explored in D&D before.
Instead, I'd go with the idea that bards can name things, and those names stick--at least long enough for their magic to work on. A lot of the times, the bard will name a creature "Mud" because the goal is to kill/defeat that creature. It's similar in concept but not identical.
Something like that. Bard magic isn't true truenaming as they don't actual say the truenames.
It's a derivative of Truenaming like Traditional Spellcasting and Pact Magic that is safe for mortals. However it is closer in application but farther is accuracy.
But like you said, bards say what something is or give something a name to raise or lower its importance to fate temporarily. Like you said, bard give things new names and the reality warps to merge the two for a time.