How do I display logged-in username IF logged-in?

I’m working on creating some text that says ‘Login’ to users that are not logged in, and the user’s username or display name when logged in.

It seems like it should be an easy problem to solve, and I’ve found the following two bits of code on the wordpress codex that each do half of what I am looking for, but I haven’t figured out how to combine them (without breaking the site).

Is this the correct direction, or way off base?

To check if the user is logged in and display something different depending:

<?php if ( is_user_logged_in() ) {
    echo '{username code here}';
} else {
    echo 'Login';
}
?>

To get and display the current user’s information:

<?php global $current_user;
wp_get_current_user();
echo 'Username: ' . $current_user->user_login . "n";
echo 'User display name: ' . $current_user->display_name . "n";
?>