Is there a way to get the project folder name only on a Github action?

In addition to @Samira response, you could also use ${GITHUB_REPOSITORY#*/} to get the repository name, since it will cut all before the / prefix.

For e.g., at my workflow I use:

- run: echo ::set-env name=TF_VAR_instance_label::${GITHUB_REPOSITORY#*/}-${GITHUB_SHA:0:7}

github context also contains event data, from where you can easily read some more detailed info. In this case, ${{ github.event.repository.name }} will give you only repo-name part.

It might be a good idea to create testing workflow/job to print all context data until you're familiar with them, see Example printing context information to the log file.

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As for replacing text, you can always dedicate one of first steps to prepare everything you need later with either ::set-env or ::set-output. You just need to print name/value in specific format, so you can use any shell you're familiar with to manipulate text while doing that:

# All steps after this one will have env variable `GHA_BRANCH` passed to them.
- run:   echo ::set-env name=GHA_BRANCH::$(echo $GITHUB_REF | awk -F / '{print $3}')
  shell: bash