I hate to pull out the true Scotsman card, but really. Neither of them are in the same hemisphere as a Rowling for popular fame. Neither are American, either, and I strongly suspect that’s a piece of the answer.
I’m pretty sure it was Silverberg.
I reviewed an anthology, Aurora: Beyond Equality, that had new stories by both Raccoona Sheldon and James Tiptree. I hated the Sheldon story, but loved the Tiptree. Fortunately for my reputation, the Sheldon story was “Your Faces, O My Sisters! Your Faces Filled of Light!” a dud that’s never been reprinted outside of a Tiptree collection, while the Tiptree story was “Houston, Houston, Do You Read?” which became an award winner and one of the most celebrated stories in the field. Whew! Dodged a bullet there.
Harry Turtledove came up with the name H.N. Turteltaub when he began writing historical fiction. It wasn’t designed to hide his identity (turteltaub is the German word for turtledove). But Turtledove was an established writer in science fiction and fantasy and he was worried that if his historical fiction was published under his real name and didn’t sell, the lower sales would hurt his future book orders. So he invented a pen name so he could keep his historical fiction separate from his other work.
Your OP asks about literature but the title is more ambiguous, so I’ll cite a non-literature case.
Satoshi Nakamoto is the pseudonym used by the author of the Bitcoin software. Despite tremendous effort and interest, no one knows who he (or she) is. He’s worth the better part of a billion dollars due to the software, so in terms of success he’s (in some sense) the equivalent of a Rowling or King, even if the name is not that widely known by the public.
He started writing as Eric G. Iverson, feeling that people would think his real name was a pseudonym. And he was right: there was a letter to Analog complaining about a story and saying that “Turtledove” was an obvious pseudonym to make the point of the story.