Wpdb get->results to out the the month from the db

You could use the MONTHNAME(dato) on your select Like

$rows = $wpdb->get_results( "SELECT MONTHNAME(dato) as month_name, avg(fiske_vaegt) as fiske_vaegt 
    FROM `wp_registreringer`
    WHERE MONTH(dato) = 11 AND YEAR(dato) = 2017;");

and access it like this echo $row->month_name