If a repository is cloned using the HTTPS URL instead of the SSH URL, there will be a prompt for a GitHub username and password. If the SSH URL is used then there will be no prompt for a password if SSH is already set up on GitHub.
You can check what is being used, (HTTPS or SSH), with the following code in Terminal:
git remote -v
To change the repository origin replace USERNAME with the username and REPOSITORY with the repository name when using the following code:
git remote set-url origin firstname.lastname@example.org:USERNAME/REPOSITORY.git