When you pay your ghostwriter, you have a contract that states what the circumstances are. You can pay for the ability to publish their product under a different name. You can pay them to sign away their authorship rights; you can pay them to sign away their future rights to royalties; you can pay them to not use the pseudonym on their own. They agree to that, in exchange for $x.
So, for example, there is no Carolyn Keene. Edward Stratemeyer, the publisher, sketched out the characters and the plots, and handed it off to Mildred A. Wirt for 23 of the first 30 Nancy Drew books, to actually do the hard work of putting it all together. Plenty of other ghostwriters have written under the Carolyn Keene pen name— but it’s all a secret.
Stratemeyer did the same thing with the Dana Girls series, also under the Carolyn Keene pen name. Leslie McFarlane did the first four books. Mildred Wirt wrote 5-16. Stratemeyer’s daughter, Harriet, did a lot of the rest of the series, but other ghostwriters contributed as well.
Stratemeyer did the same thing with the Hardy Boys series, under the Franklin W. Dixon pen name. Leslie McFarlane wrote 19 of the first 25 stories. There were about 7 other ghostwriters who worked on it over the next few decades.
Looking at more modern works, you have the Warriors series (about cats). It’s written by Erin Hunter-- but Erin Hunter is a collective pseudonym for several writers. Victoria Holmes writes the outlines; Kate Cary, Cherith Baldry, and Tui T Sutherland do the work of writing. Later on, when they started writing series about bears and dogs, they brought in Gillian Philip, Inbali Iserles, and Rosie Best. In that case, it was easier to use a collective pseudonym so that the series would be shelved together in a library under a single name, rather than all over the place.
So— if you feel a bit awkward about claiming someone’s work as your own, even if you’re paying them for it-- why not choose a pseudonym for your collaboration? You’d still pay them. But then you wouldn’t feel weird about giving the wrong impression.