MySQL Deltag og få alle relationer, selvom 0

for at venstre join skal være i kraft, skal du flytte betingelsen earned_trophys.user_id = 1 ind i on klausul i stedet for where .

select
    trophy.name,
    earned_trophys.user_id,  
    count(user_id) as temp
from
    trophy
left join
    earned_trophys
on
    trophy.trophy_id = earned_trophys.trophy_id and earned_trophys.user_id = 1
group by
    name