The ‘heroku’ part is the name of the remote that you have setup – when you create a heroku app the first time it creates a git remote call ‘heroku’ pointing at your application – if you type ‘git remote’ within your project it will show you the remote endpoints. There’s nothing locking you into using ‘heroku’ as the name of the remote – if you have multiple environments for your application you may have remotes named production or staging for example.
The ‘master’ part is the local branch you wish to push to the remote. If you develop in a feature branch for example named ‘myfeature’ and you want to deploy that to heroku you would do;
git push heroku myfeature:master
the additional :master here is saying push my local myfeature branch into the master branch on the remote – note: heroku can only deploy from the master branch.
If you rename an app the heroku git remote url will change – do a git remote -v which will show you the git repo your app is using, you will probably need to delete your old heroku origin and add the new one, git remote rm heroku then git remote add heroku git@newgitpathfromcontrolpanel
To learn more about Git I would recommend this book