The help text for the "Add Tag" section of the "Git Publisher" Post-Build Action states:
Specify tags to push at the completion of the build.
If the "Create Tag" or "Update tag" option is selected, the tag will be created or updated and pushed at the completion of the build, and the push will fail if a tag with the given name already exists. If the "Create Tag" option is not selected, the push will fail if the tag does not already exist.
Environment variables may be used in the tag name - they will be replaced at build time.
The repository name needs to be one of the repositories configured in the SCM section above.
I have found that environment variables can be used in the tag message, but not the name. I don't understand why the plug-in would require the tag name to be hard-coded - who would go configure the job before each build to add a hard-coded tag name?