Check your remotes via git remote -v.
https:// URLs will always ask for a password, unless you configure a credential helper. More info on that in this question.
The simplest solution for password-less git access would be to use the git remote set-url command and set an SSH url for the existing repo.
In your case, git remote set-url origin git@github.com:name/repo.
Then you should be able to git push origin <branch> without being asked for a password.