No, but it means they and only they can study it, do gain of function research on it, make vaccines for it, etc. Unless the other person wants to pay royalties.
This is a very relevant discussion.
And the reason it is called “19” is that somebody named it. That somebody had a patent.
Forgot to mention The CDC sent funds to Wuhan for gain function studies once it was banned in Murica.
I might be wrong but I believe the name of the Covid virus is chosen by an international organization, like WHO, and the number 19 refers to the year it was first identified. You cannot get a patent on a naturally occurring virus but it is possible if you have genetically altered a natural virus. This patent from 2010 is not the Covid virus and I haven’t heard of a patent for Covid as yet but I believe a coronavirus was being attempted here in a biolab in North Carolina with the intent of making it more transmissible to test mice and, after this kind of jiggering here was prohibited, the strain was sent to Wuhan to continue the gain-of-function work.