When I updated my world from 1.15.2 to 1.16.1, most of the decorative player heads I had around my house turned to the default Steve skin! Strange thing though, a few did not change. What's going on? Screenshots include the same room in 1.15.2 and 1.16.1.
However, I have a copy of the same world that I have been regularly using to test out snapshots, and when I played that copy in 1.16.1, the heads were unchanged. So, something about the big jump from 1.15.2 to 1.16.1 did it!
In the version where the player heads are working, I think you mentioned that on 1.15.2 they were okay.
Can hold CTRL + ALT and press the middle mouse button on the player head, to get the block you're pointing at with NBT.
And then put it on the first inventory slot and type in
Also the copy of the world, what's the original version and how does it come you played it on 1.16.1 but it was on 1.15.2?
Similar issues:
MC-162453
MC-190537