Doesn't seem to be a way to do it from the command line, and when I do this from the site, I run into this issue when I try to git push heroku master:
! No such app as [previous app name].
Is this as simple as changing how I point to the app in git?
Why use all caps?
heroku apps:rename my_new_app_name
Here is a great place to find out more:
How to rename your Heroku application
In case anyone is curious this method does not require any further configuration, your modifications should be immediate. At the time of this writing I was able to change the name of my app in seconds, and then do so again if I wished. Hope this helps.