The first menu item typically is the parent item and shares the name with that item, you can however manually update the entry directly in the $submenu
variable, like so..
add_action( 'admin_menu', 'jp_create_admin_pages' );
function jp_create_admin_pages() {
global $submenu;
add_menu_page('Members','Members','manage_options','members','jp_handle_admin_members');
add_submenu_page('members','Membership Types','Membership Types','manage_options','membership_types','jp_handle_admin_membership_types');
$submenu['members'][0][0] = 'All Members';
}
That way your parent keeps the original name, whilst the first subitem has another.
Hope that helps.