No, you cannot rename an Azure Resource Group, all you can do is move an existing resource group to a new resource group.
In the case of Azure Web Apps, you can only move all websites related resources in one invocation. This "all websites related resources" includes all websites, app hosting platforms, and certificates.
From the Portal
Use the "Move" tab for viewing resource groups
Clicking the "Move" tab will show this, which allow you to choose or create a new group:
Now Using Azure Powershell
use the Move-AzureRmResource powershell cmdlet.
The command for this:
Get-AzureRmResource -ResourceGroupName <sourceResourceGroupName> | Move-AzureRmResource -DestinationResourceGroupName <destResourceGroupName>
Using the Rest API:
Another way to is you use the MoveResource Rest API or an ArmClient.
This is how you will make an API call:
POST
https://<endpoint>/subscriptions/{subscriptionId}/resourcegroups/{resourceGroupName}/moveResources?api-version={api-version}
Where {resourceGroupName} is the source resource group. If you are using the ArmClient tool, then it will just take care of the endpoint.
Request Body:
{
"targetResourceGroup": "/subscriptions/{subscriptionId}/resourceGroups/{targetResourceGroupNameName}",
"resources":
[
"/subscriptions/{id}/resourceGroups/{source}/providers/{namespace}/{type}/{name}",
"/subscriptions/{id}/resourceGroups/{source}/providers/{namespace}/{type}/{name}"
]
}
If you want to have a successful Azure career then you can visit the Microsoft Azure tutorial for Beginners and join AZ-104 certification.