Update public pool names (#43681)

.azure/pipelines/jobs/default-build.yml

@@ -112,14 +112,14 @@ jobs:
           vmImage: ubuntu-18.04
         ${{ if or(eq(parameters.useHostedUbuntu, false), and(eq(variables['System.TeamProject'], 'internal'), notin(variables['Build.Reason'], 'Manual', 'PullRequest', 'Schedule'))) }}:
           ${{ if eq(variables['System.TeamProject'], 'public') }}:
-            name: NetCore1ESPool-Svc-Public
+            name: NetCore-Svc-Public
             demands: ImageOverride -equals Build.Ubuntu.1804.Amd64.Open
           ${{ if eq(variables['System.TeamProject'], 'internal') }}:
             name: NetCore1ESPool-Svc-Internal
             demands: ImageOverride -equals Build.Ubuntu.1804.Amd64
       ${{ if eq(parameters.agentOs, 'Windows') }}:
         ${{ if eq(variables['System.TeamProject'], 'public') }}:
-          name: NetCore1ESPool-Svc-Public
+          name: NetCore-Svc-Public
           demands: ImageOverride -equals 1es-windows-2022-open
         ${{ if eq(variables['System.TeamProject'], 'internal') }}:
           name: NetCore1ESPool-Svc-Internal

eng/common/templates/job/source-build.yml

@@ -46,7 +46,7 @@ jobs:
     # source-build builds run in Docker, including the default managed platform.
     pool:
       ${{ if eq(variables['System.TeamProject'], 'public') }}:
-        name: NetCore1ESPool-Public
+        name: NetCore-Public
         demands: ImageOverride -equals Build.Ubuntu.1804.Amd64.Open
       ${{ if eq(variables['System.TeamProject'], 'internal') }}:
         name: NetCore1ESPool-Internal

eng/common/templates/job/source-index-stage1.yml

@@ -28,7 +28,7 @@ jobs:
   ${{ if eq(parameters.pool, '') }}:
     pool:
       ${{ if eq(variables['System.TeamProject'], 'public') }}:
-        name: NetCore1ESPool-Public
+        name: NetCore-Public
         demands: ImageOverride -equals windows.vs2019.amd64.open
       ${{ if eq(variables['System.TeamProject'], 'internal') }}:
         name: NetCore1ESPool-Internal