There isn't an easy way to do what you want, from what I can find in the GitLab documentation and some open issues that they have.

Here is an issue that describes something similar to what you want:

https://gitlab.com/gitlab-org/gitlab-runner/issues/3540

Here is what I think is GitLab's goal with how to register runners:

https://gitlab.com/gitlab-org/gitlab-ce/issues/40693

I believe that the only thing that you can't change from the .toml file is the name of the runner, and maybe not the tags either. Then name is only created when you register the runner. I read something somewhere that you can change the tags of a shared runner, but I can't find it now.

Here is a workaround to make the process of registering a bit more automatic:

https://gitlab.com/gitlab-org/gitlab-runner/issues/3553#note_108527430

He used this API:

curl --request POST "https://gitlab.com/api/v4/runners" --form "token=<registration-token>" --form "description=test-1-20150125-test" --form "tag_list=ruby,mysql,tag1,tag2"

Then he got the following response back:

{"id":401513,"token":"<runner-token>"}

He could then inject the runner-token into his already pre-made .toml file.

For you, it would have been possible to use the registration token for your group, and then to write in the description/name of the runner and the tags. You could then have re-used your config.toml and only changed the runner-token, and it should have worked.