with name_tree as (
select id, parent_id, name
from the_unknown_table
where id = 1 -- this is the starting point you want in your recursion
union all
select c.id, c.parent_id, c.name
from the_unknown_table c
join name_tree p on p.parent_id = c.id -- this is the recursion
)
select *
from name_tree
where id <> 1; -- exclude the starting point from the overall result
SQLFiddle:http://sqlfiddle.com/#!3/87d0c/1