Unfortunately, you are not allowed to add custom tags for the Managed Resource Group created in Azure Databricks using Azure portal/PowerShell/CLI.
Reason: By default, you cannot perform any write operation on the managed resource group.
If you try to modify anything in the managed resource group, you will see this error message:
{"details":[{"code":"ScopeLocked","message":"The scope '/subscriptions/xxxxxxxxxxxxxxxx/resourceGroups/databricks-rg-chepra-d7ensl75cgiki' cannot perform write operation because following scope(s) are locked: '/subscriptions/xxxxxxxxxxxxxxxxxxxx/resourceGroups/databricks-rg-chepra-d7ensl75cgiki'. Please remove the lock and try again."}]}
Possible way: You can specify tags as key-value pairs when while creating/modifying clusters, and Azure Databricks will apply these tags to cloud resources.
Cluster tags allow you to easily monitor the cost of cloud resources used by various groups in your organization. You can specify tags as key-value pairs when you create a cluster, and Databricks applies these tags to cloud resources like VMs and disk volumes.
For convenience, Databricks applies four default tags to each cluster: Vendor, Creator, ClusterName, and ClusterId. You can add custom tags when you create a cluster. To configure cluster tags:
- On the cluster configuration page, click the Advanced Options toggle.
- At the bottom of the page, click the Tags tab.

- Add a key-value pair for each custom tag. You can add up to 45 custom tags.
Now you can see the previously added tag in the portal:

Reference: Azure Databricks - Cluster Tags.
Hope this helps.