Compare the following in your example:
Given that Scott is a project manager, and the stackoverflow integration project has never been registered with the system. When Scott registers a stackoverflow integration project that indicates Jane as a member of the project, then the stackoverflow integration project should appear in the list of Jane projects
VS:
For the project manager and an unregistered project, when the Project Manager registers the project and indicates a team member, then the project should appear in the list of projects of the project participants.
Note that the wording of the second example above is not too different from the first example that you indicated in your question, but it is slightly different, so it reads as if it is a little more complete. I think that this is something that you might feel is missing, and if so, I would consider it as a kind of “smell of history,” and if so, I will continue to ask questions and rewrite until while the story / script feels more complete.
Personally, I think that using persona distracts me from the task, and I don’t like it when my test code ends up littered with text that cannot be read as if it refers to what I'm testing. If, on the other hand, you use a data-based approach, and for this purpose you are defining some kind of data structure, then it makes sense to populate this structure with names that may make sense within the area in which they are tested.
I think one of the risks with using a person is that they can sometimes be a substitute for the lazy method name or even worse, because for bored programmers you can try to introduce a little humor into your code. Not that I thought it was bad to have a little fun with your names, but if they don't give value to stake holders, then they shouldn't be used.
Another thought arises with me, although you can have the best of both worlds. If you indicate your user identity as the data for the plot scenario, then it will be useful for you to keep your code clean and to such an extent, but you can make the conclusion more specific in terms of the actual test execution. For example:
new Story("Project Registration") .InOrderTo("allow project members to collaborate over a project") .AsA("project manager") .IWant("to be able to register new projects") .WithScenario("New Project Registration") .Given(AProjectManager, "Scott") .And(AnUnRegisteredProject, "Qaru Integration") .When(TheProjectManagerRegistersTheProject) .And(TheProjectManagerSpecifiesATeamMember, "Jane") .Then(ThenTheProjectShouldAppearInTheTeamMembersListOfProjects) .Execute();