Rights?
Now, I’m not a lawyer, so don’t take this as legal advice. This also isn’t exactly an exhaustive description of your rights, just the basic idea:
As the producer of your audio-book, my attachment to your book ends after production. I’ll have my name on it forever, but that’s basically it. Control and rights to your book will remain entirely between you and your publisher, or whomever else you have legally binding contracts with. The only thing you’ll have to give up when hiring me or any other narrator is the money to pay our fees, and space in your audiobook for our names.