Paracetamol was coined in 1956, acetaminophen was coined in 1955[1]. The world pharmaceutical stage was a bit less globalized back then, so splits in naming like this just happened. They're both contractions of the full chemical name, so it's hard to argue one is more correct than the other. At this point the names are too entrenched in their respective countries, so changing them would only cause mass confusion and likely overdoses due to people not understanding what they're taking.

[1]: https://en.wikipedia.org/wiki/Paracetamol#Naming

What parts of the US use paracetamol? I’ve lived on both coasts and the Midwest and haven’t ever seen anything but acetaminophen.

I've live for all my life in a lot of places in the US and "Paracetamol" was never used. I'd never heard that term until this HN thread.