diff --git a/CHANGELOG.md b/CHANGELOG.md
index 9e94916c3..3ad7b6ffb 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -62,6 +62,8 @@
   - Fixed minor typos in comment-based help.
   - Fixed minor typos in comment.
   - Style cleanup in code and tests.
+  - Updated description for parameter Name in README.md and in comment-based help
+    ([issue #1034](https://github.com/PowerShell/SqlServerDsc/issues/1034)).
 - Changes to SqlAlias
   - Fixed issue where exception was thrown if reg keys did not exist
     ([issue #949](https://github.com/PowerShell/SqlServerDsc/issues/949)).
diff --git a/DSCResources/MSFT_SqlAGReplica/MSFT_SqlAGReplica.psm1 b/DSCResources/MSFT_SqlAGReplica/MSFT_SqlAGReplica.psm1
index e9cc9ddda..fb0fc0c2a 100644
--- a/DSCResources/MSFT_SqlAGReplica/MSFT_SqlAGReplica.psm1
+++ b/DSCResources/MSFT_SqlAGReplica/MSFT_SqlAGReplica.psm1
@@ -7,7 +7,8 @@ Import-Module -Name (Join-Path -Path (Split-Path (Split-Path $PSScriptRoot -Pare
         Gets the specified Availability Group Replica from the specified Availability Group.
 
     .PARAMETER Name
-        The name of the availability group replica.
+        The name of the availability group replica. For named instances this
+        must be in the following format ServerName\InstanceName.
 
     .PARAMETER AvailabilityGroupName
         The name of the availability group.
@@ -109,7 +110,8 @@ function Get-TargetResource
         Creates or removes the availability group replica in accordance with the desired state.
 
     .PARAMETER Name
-        The name of the availability group replica.
+        The name of the availability group replica. For named instances this
+        must be in the following format ServerName\InstanceName.
 
     .PARAMETER AvailabilityGroupName
         The name of the availability group.
@@ -465,7 +467,8 @@ function Set-TargetResource
         Determines if the availability group replica is in the desired state.
 
     .PARAMETER Name
-        The name of the availability group replica.
+        The name of the availability group replica. For named instances this
+        must be in the following format ServerName\InstanceName.
 
     .PARAMETER AvailabilityGroupName
         The name of the availability group.
diff --git a/README.md b/README.md
index e67d1b2b2..d966afeb2 100644
--- a/README.md
+++ b/README.md
@@ -370,7 +370,7 @@ Always On Availability Group Replica.
 #### Parameters
 
 * **`[String]` Name** _(Key)_: The name of the availability group replica. For named
-  instances this must be in the following format SQLServer\InstanceName.
+  instances this must be in the following format ServerName\InstanceName.
 * **`[String]` AvailabilityGroupName** _(Key)_: The name of the availability group.
 * **`[String]` ServerName** _(Required)_: Hostname of the SQL Server to be configured.
 * **`[String]` InstanceName** _(Key)_: Name of the SQL instance to be configured.