support: How to control the domain name (not a custom domain)?

Checklist

[X] I am using the latest version of this action.
[X] I have read the latest README and followed the instructions.
[X] I have read the latest GitHub Actions official documentation and learned the basic spec and concepts.

Describe your question

When I deploy GitHub pages, I get a domain name https://redesigned-bassoon-19zzy9p.pages.github.io/. Is there any way to control redesigned-bassoon-19zzy9p part? Make it predictable and dependent on variables.

Because next, I want to use https://github.com/marketplace/actions/github-checks to show some images from GitHub pages in summary. So I need to know the domain name.

Relevant links

Public repository:
YAML config:

      - name: Deploy
        uses: peaceiris/actions-gh-pages@v3
        if: success() || failure()
        with:
          personal_token: ${{ secrets.PRIVATE_KEY }}
          user_name: 'devfaculty'
          user_email: 'devfaculty@prjctr.com'
          publish_dir: ./
          force_orphan: true

YAML workflow:

Relevant log output

No response

Additional context.