How to join to the same table multiple times? I have two tables, "hierarchy_table" and "name_table".

The hierarchy table contains an object which has multiple parents and children. Each parent and child is referenced by id.

|  object_id  |  parent_id_1  |  parent_id_2  |  child_id_1  |  child_id_2  |
-----------------------------------------------------------------------------
|     1234    |      9999     |      9567     |     5555     |     5556     |
-----------------------------------------------------------------------------


Each object id in the hierarchy_table has an entry in the name_table:

|  name_id  |    name    |
--------------------------
|   1234    |   ABCD     |
--------------------------
|   9999    |   ZYXW     |
--------------------------
| ...


How do I join each id in the hierarchy_table to the name_table multiple times so that I can have a result where every name is populated? 

Like this:

|   object    |   parent_1    |   parent_2    |   child_1    |   child_2    |
-----------------------------------------------------------------------------
|     ABCD    |      ZYXW     |      BBBB     |     CCCC     |     DDDD     |
-----------------------------------------------------------------------------


Note:  the table names in the example are just for clarity / simplicity, the real names have proper names.
The hierarchy_table has 5 columns that all reference the name_table, so you need 5 joins. It may be better to use LEFT joins instead of INNER, in case some of these columns are nullable and you still want the rows returned:

SELECT 
    o.name  AS object, 
    p1.name AS parent_1, 
    p2.name AS parent_2, 
    c1.name AS child_1,  
    c2.name AS child_2 
FROM 
    hierarchy_table AS h
  LEFT JOIN name_table AS o   ON h.object_id   = o.name_id
  LEFT JOIN name_table AS p1  ON h.parent_id_1 = p1.name_id  
  LEFT JOIN name_table AS p2  ON h.parent_id_2 = p2.name_id
  LEFT JOIN name_table AS c1  ON h.child_id_1  = c1.name_id 
  LEFT JOIN name_table AS c2  ON h.child_id_2  = c2.name_id ;