Esse é um requisito incomum, mas se você insistir, teria que usar sql dinâmico.
SET @curdate = CURDATE();
SET @sql = CONCAT('SELECT whatever AS "', @curdate, '" FROM whatever');
PREPARE stmt FROM @sql;
EXECUTE stmt;
DEALLOCATE PREPARE stmt;
SET @curdate = CURDATE();
SET @sql = CONCAT('SELECT whatever AS "', @curdate, '" FROM whatever');
PREPARE stmt FROM @sql;
EXECUTE stmt;
DEALLOCATE PREPARE stmt;
