Feat(infra) - Make chained e2e workflow run e2e tests (#11521)

Co-authored-by: gemini-cli-robot <gemini-cli-robot@google.com>

.github/workflows/trigger_e2e.yml

@@ -10,6 +10,20 @@ on:
         type: 'string'
 
 jobs:
+  save_repo_name:
+    runs-on: 'gemini-cli-ubuntu-16-core'
+    steps:
+      - name: 'Save Repo name'
+        env:
+          # Replace with github.event.pull_request.base.repo.full_name when switched to listen on pull request events. This repo name does not contain the org which is needed for checkout.
+          REPO_NAME: '${{ github.event.repository.name }}'
+        run: |
+          mkdir -p ./pr
+          echo '$REPO_NAME' > ./pr/repo_name
+      - uses: 'actions/upload-artifact@ea165f8d65b6e75b540449e92b4886f43607fa02' # ratchet:actions/upload-artifact@v4
+        with:
+          name: 'repo_name'
+          path: 'pr/'
   trigger_e2e:
     name: 'Trigger e2e'
     runs-on: 'gemini-cli-ubuntu-16-core'