@Rob McNees Sorry for being late to respond to this question. It is not recommended to use the same naming convention for resource groups used in Azure Site Recovery for disaster recovery purposes. This is because the resource group name is used as part of the URL for your authoring and prediction endpoint queries, and it is important to have a unique name for each resource group to avoid conflicts.
In addition, it is a best practice to set up and consistently apply good naming conventions across all Azure resources from resource groups to each resource type. A good naming convention communicates purpose and helps lay a solid foundation for discoverability and supportability.
Microsoft provides guidance around naming conventions for Azure resources, including abbreviations for Azure resources and the Azure Naming Tool, which generates Azure-compliant names, helps you standardize on names, and automates your naming process.
Adding few source links below:
Hope this helps!