If I understand your question correctly, you first need to create a git hook to start a new build. This part is covered in the answer. How can I respond to new tags in git hooks? "though, if you use something like GitHub, BitBucket or Gitlab, then there may be other ways around this.
Then, when the assembly begins, there is an assembly number that is provided as the variable ' BUILD_NUMBER ' in Jenkins. If you want to include the git tag name, so you can use it in a script, then there seem to be several ways:
Typically, these plugins will create an environment variable that can be used by your scripts. I do not give more specific examples, since I do not know your exact tool.
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