если правильно понял задачу, то так:
SELECT artist.id, artist.name, GROUP_CONCAT(style.name), count(artist_style.style_id) as cnt_style
FROM artist
LEFT JOIN artist_style ON artist_style.artist_id = artist.id
LEFT JOIN style ON artist_style.style_id = style.id
GROUP BY artist.id
HAVING cnt_style > 1
