What is the name of the round metal bit at the top of a bathtub drain?
The following is UK terminology.
As a unit it's a 'bath waste', but that includes the part it's screwed to underneath and quite often the pipe &amp; overflow linkage too - everything above the trap.
If you want only the part you can see in the photo, it's a 'jumper plate' - but be careful, because a jumper is also a tap [faucet] washer.
I have to admit to having to look up what just this bit is called. I've never dealt with anything smaller than the entire waste, which also tends to be how you buy them; as complete sets.
If you were to visit a merchant's in person, you could get away with just calling it a 'plug hole' &amp; wait for them to ask you which bit of it you require &amp; what size. Bath wastes tend to be 40mm standard, though ask for 'inch &amp; a half' as we Brits seem to have hung onto that as a definition.
BTW, be very very careful of just unscrewing the jumper plate unless you can reach underneath to hold it up. That's not a predicament you want to be in if you have tiled the bath sides, or can't come in from the ceiling below. Your question doesn't make it clear just what access you have or quite what you intend to do.