Is it possible to rename app service plan in Azure Portal ?
Answer is No, you can not rename the app service plan once it is created. Alternatively, you can create a new app service plan in the same region and same resource group where your web app exists and then remap your web app to a new app service plan and delete the old one.
Refer Below screenshots.
Fig 1 - App Service Plan in West Europe
Fig 2 - App Service Plan associated with 2 Apps
Fig 3 - Create a new App Service Plan in same Region and Resource Group
Now select your web app and go to “Change App Service Plan” from the App Service Plan section on the left menu to map to newly created app service plan.
Fig 4 - Change App Service Plan for Web App
Fig 5 - Web App with new App Service Plan