Update pipeline job names and dependencies (#4789)

- Fixes #4643

.azure-pipelines/client.yml

@@ -5,7 +5,7 @@ variables:
   NodeVersion: '10.x'
 
 jobs:
-  - job: 'Publish'
+  - job: 'Build'
 
     pool:
       vmImage: 'ubuntu-16.04'
@@ -16,8 +16,8 @@ jobs:
           versionSpec: '$(NodeVersion)'
         displayName: 'Install Node.js $(NodeVersion)'
 
-      # Reduce build time by only installing the "npm-run-all" package, which is the minimum required to run the
-      # composite script commands.
+      # Rather than running "npm install" in the repo root, reduce build time by only installing the "npm-run-all" package,
+      # which is the minimum required to run the composite script commands.
       - task: Npm@1
         inputs:
           command: 'custom'
@@ -44,15 +44,21 @@ jobs:
         displayName: 'Copy Package'
 
       - task: PublishBuildArtifacts@1
-        displayName: 'Publish Package'
+        condition: succeededOrFailed()
+        displayName: 'Publish Artifacts'
+        inputs:
+          artifactName: packages
 
   - job: 'Analyze'
 
+    dependsOn:
+      - 'Build'
+
     pool:
       vmImage: 'ubuntu-16.04'
 
     steps:
-        # sudo is required for pip install, as a console_entrypoint shim needs to be placed in bin
+      # sudo is required for pip install, as a console_entrypoint shim needs to be placed in bin
       - script: |
           pip install setuptools wheel
           sudo pip install doc-warden
@@ -87,7 +93,7 @@ jobs:
   - job: 'Test'
 
     dependsOn:
-      - 'Publish'
+      - 'Build'
 
     strategy:
       matrix:
@@ -142,7 +148,7 @@ jobs:
 
     pool:
       vmImage: '$(OSVmImage)'
-      
+
     steps:
       - task: NodeTool@0
         inputs: