call adminbar greeting in other place

If I got you right, then you don’t want to show other details than the greetings in the front end admina bar. If that is so then you can use Remove Node to make this work.

You can use it like below for only greetings and other options in it to display

First remove the below line

add_filter('show_admin_bar', '__return_false');

Use the below in your active theme’s functions.php file.

add_action( 'admin_bar_menu', 'wpse_remove_node', 999 );
function wpse_remove_node( $wp_admin_bar ) {
    $wp_admin_bar->remove_node( 'wp-logo' );
    $wp_admin_bar->remove_node( 'site-name' );
    $wp_admin_bar->remove_node( 'updates' );
    $wp_admin_bar->remove_node( 'comments' );
    $wp_admin_bar->remove_node( 'new-content' );
    $wp_admin_bar->remove_node( 'edit' );
}

The above will remove all the basic nodes from the admin bar from the front end and even if you have other nodes added due to plugins/theme, then you remove those using the same way.