BuddyPress.org

Howdy. There is probably some slick way to unregister a widget and then re-register it again with a different name but looks like you need the widget $id. Wherever that comes from. Anyway, /mu-plugins/bp-core/bp-core-widgets.php line numbers 12/13:

register_sidebar_widget( __('Members', 'buddypress'), 'bp_core_widget_members');

register_widget_control( __('Members', 'buddypress'), 'bp_core_widget_members_control' );

‘Members’ to ‘Whatever’. They’ll vanish from the page(s) and you’ll have to add ’em back where you want them.