GitHub took the "pull request" terminology from Git. A kernel developer (say) would have a bunch of changes ready in their local Git server and would request a pull from Linus, hence a pull request. There's literally a command for it:

https://git-scm.com/docs/git-request-pull

The command is so old it's still written in shell:

https://github.com/git/git/blob/master/git-request-pull.sh

It was first added July 27, 2005:

https://github.com/git/git/commit/ab421d2c7886341c246544bc8d...

https://lore.kernel.org/git/20050726073036.GJ6098@mythryan2....

But even then, it simply codified existing terminology.

Ah, someone else did the research, so minimally BitKeeper had the "pull" command first and the term "pull request" falls naturally from that:

https://rdnlsmith.com/posts/2023/004/pull-request-origins/