Change the default blog post post attribute template name from “default template” to something else

Yes, and one way is by accessing the global $post variable and then check if it’s for a post of the post type (or any custom post types). E.g.

add_filter( 'default_page_template_title', function ( $label ) {
    global $post;
    if ( 'post' === get_post_type( $post ) ) {
        return __( 'new default name for posts only', 'your_text_domain' );
    }

    return $label;
} );

Or the other way is by checking if the current screen’s ID is edit-post (or edit-<post type>), and you’d just need to change the above if condition to:

if ( 'edit-post' === get_current_screen()->id )