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select name, 
       count(case when value <= 5 then 1 end) as "0-5",
       count(case when value > 5 and value <= 10 then 1 end) as "5-10",
       count(case when value > 10 and value <= 15 then 1 end) as "10-15"
from the_table
group by name;

Mit der kommenden Version 9.4 kann dies etwas lesbarer geschrieben werden:

select name, 
       count(*) filter (where amount <= 5) as "0-5",
       count(*) filter (where value > 5 and value <= 10) as "5-10",
       count(*) filter (where value > 10 and value <= 15) as "10-15"
from the_table
group by name;