Encontrei uma solução sozinho, com uma subconsulta:
SELECT
SUBSTRING_INDEX(
GROUP_CONCAT(DISTINCT name ORDER BY CountName DESC SEPARATOR '||')
, '||', 1),
address,
postalcode,
place,
phone
FROM (
SELECT name, address, postalcode, place, phone , COUNT(name) AS CountName
FROM addresses
GROUP BY name, postalcode, phone
ORDER BY COUNT(name) DESC
) as a
GROUP BY postalcode, phone
Gostaria de saber se isso pode ser feito sem uma subconsulta.