At this point our recommendation is to move resources into a new Resource Group with the new name.
Thank you for voting on this suggestion. It is now completed and can be done via custom Azure Policy. Here is a sample custom policy to apply a specific tag at the RG and have them inherited by the Resources in that RG: https://github.com/Azure/azure-policy/tree/master/samples/ResourceGroup/copy-resourcegroup-tag
Tag inheritance for existing resources is something that we plan to add support for in 2019.