How to rename existing Azure Logic App?

You cannot rename web app as far as I'm aware. You can redeploy using different name and then delete existing one.

Select the LogicApp, clone it with a new name, delete the old one.

Existing logic app cannot be renamed. we can clone the existing logic app with a new name. However,the cloned logic app will be created in the same resource group of the existing logic app. we can change the resource group or location of the logic app once the cloning is completed, but in order to avoid any run time error we need to update the subscription/Resource group name or id in the code view.