No. Your Paratext 8 registration will work in Paratext 9. When you install Paratext 9, it will detect your registration info if Paratext 8 is installed on your computer.
Important Announcement for Paratext 8 Users
Please read our important announcement for Paratext 8 users. Ongoing support for Paratext 8 ended on Dec 31, 2021. Paratext 8 will continue to work with Paratext 9, but our focus is now on improving Paratext 9.
We hope you are able to upgrade to Paratext 9 soon.