Azure portal rename resources
Using the new portal, you can move a resources in a resource group to another resource group. The capability only became available recently. You can read more about it here: Move resources to new resource group or subscription
Unfortunately it cannot be done. Neither on resource name or on resource group name.
The correct naming ruling put in place from the very beginning is one of the most important aspects. Try to define yourself as early as possible the criteria for that.
If not, working with ARM templates may ease your pain by helping you redeploy "bad" resources faster and easier.
The Answer is: Yes it not possible (yet?) but there is a mechnismn for doing it by deleting recreating any ressource. Now everybody would say: Are you serroius? Yes it is not that difficult!
The Azure Cli / Powershell allows you to export the whole resourcegroup Definition (except for some resources!).
--> Export the Definition,
--> rename Names in the exportet template
--> Deploy Template
--> Voila! Every resource has it's old configuration except the name.
It takes some time to get familiar to that process, but afterwars you are pretty fast rename, clone, do anything with complete ressources!