The position of those overhead chat boxes is based on where the character speaking is, so they only move as you move in relation to the NPC. And yeah, that can be annoying at times.

There are actually quite a few UI elements we can't move, though. Most of them show up in the center of the screen. (I'm particularly bothered by the blue notification window that tells us what result we got from crafting/gathering. Particularly while crafting, because it covers part of the crafting window, so when I'm crafting something repeatedly, I either have to do so blindly without checking how many materials I have left, or else I have to wait a couple seconds between each one for that notification to go away.)