I recently reinstalled GitHub Desktop (the Git client I use) and now all my commits I do to a GitLab projects show up from the username "[My mac username]@[My computer name].[Name of my router]" instead of the username I have in the GitLab installation.
What have I done wrong? How can I fix this?
Git does commits entirely locally on your machine, the site you push those commits just reads them. So your Gitlab account has nothing to do with who you're committing as. This is critically important for the integrity of who did what and when.
What you're getting is the default username from Git. The Git command line client would normally issue you a warning and instructions:
Github Desktop likely has its own config. It will use your Github identity, not your Gitlab. Make sure you're logged in at Preferences->Accounts. Also check Preferences->Advanced and make sure your Git Config identity is correct.