diff --git a/src/Monitor/Monitor/ActionGroups/SetAzureRmActionGroupCommand.cs b/src/Monitor/Monitor/ActionGroups/SetAzureRmActionGroupCommand.cs
index 79eb1dde498b..e9774f3c4e99 100644
--- a/src/Monitor/Monitor/ActionGroups/SetAzureRmActionGroupCommand.cs
+++ b/src/Monitor/Monitor/ActionGroups/SetAzureRmActionGroupCommand.cs
@@ -114,6 +114,10 @@ protected override void ProcessRecordInternal()
                 if (ParameterSetName == ByInputObject)
                 {
                     this.ResourceGroupName = this.InputObject.ResourceGroupName;
+                    if (this.Name == null)
+                    {
+                        this.Name = this.InputObject.Name;
+                    }
                     if (this.ShortName == null)
                     {
                         this.ShortName = this.InputObject.GroupShortName;
diff --git a/src/Monitor/Monitor/ChangeLog.md b/src/Monitor/Monitor/ChangeLog.md
index e892d422f126..c682d29be46c 100644
--- a/src/Monitor/Monitor/ChangeLog.md
+++ b/src/Monitor/Monitor/ChangeLog.md
@@ -19,6 +19,7 @@
 -->
 
 ## Upcoming Release
+* Fixed bug for `Set-AzActionGroup`
 
 ## Version 2.0.0
 * Fixed bug for `Set-AzDiagnosticSettings`, retention policy won't apply to all categories [#11589]