Hi,
You cannot rename an existing app service plan or web app.
What you may be able to do is create a new app service plan in same resource group, same region, with same OS as existing app service plan, and then switch the existing web app over to the new plan. This will work only some of the time which is why I used the word "may" in previous sentence.
If you give the above method a try and it succeeds you will have effectively renamed the app service plan, however, the web app name will be the same. Once you have switched the web app over to the new plan you could delete the old plan, assuming there are no other apps and you no longer need it.
Please click Accept Answer and upvote if the above was helpful.
Thanks.
-TP