Why is the project name ADSL when it is running Symmetric Prime Tuples.

ADSL usually means Asymmetric Digital Subscriber Line. The project's name is confusing.

First, Corporal launched a BOINC test from a developer.
Demis then started the SPT project.

Yes, of course, the name of the project should be changed.

Hope Corporal does it.

Would that mean detaching and re-attaching to the project?

I think it would require re-attaching since the URL would probably change. This will create a different project directory on the client.

Please stop playing with the renaming of the project. (Очень прошу - перестаньте играть с переименованиями проекта.)
It's not nice to the volunteers. (Это некрасиво по отношению к волонтерам.)
What was wrong with the name of the project "SPT@home"? (Чем вас не устраивало название проекта "SPT@home"?)

Please stop playing with the renaming of the project. (Очень прошу - перестаньте играть с переименованиями проекта.)
It's not nice to the volunteers. (Это некрасиво по отношению к волонтерам.)
What was wrong with the name of the project "SPT@home"? (Чем вас не устраивало название проекта "SPT@home"?)

The project is currently called "SPT test project".
This is displayed on the main page of the project
https://boinc.termit.me/adsl/

The current project name means that the project is in the testing and debugging stage.

The final renaming of the project will be later.

Sorry if renaming a project is inconvenient for you.

The project name in BOINC (in variable project_name) is fine as it is. The last name change wasn't as traumatic as it could have been as they kept the master_url setting the same. I don't see anything in the BOINC variables that need changing except the master_url (because it still has the adsl directory in it) but that would require possibly changing things in the server configuration. It wouldn't be worth making that change and I would leave it the way it is currently set. You can do whatever you want on the main page, that doesn't change the BOINC configuration in any way.