Get all partition names for a table

Use the first query from the answer you linked and add a simple WHERE clause to get the partitions of a single table:

SELECT
    nmsp_parent.nspname AS parent_schema,
    parent.relname      AS parent,
    nmsp_child.nspname  AS child_schema,
    child.relname       AS child
FROM pg_inherits
    JOIN pg_class parent            ON pg_inherits.inhparent = parent.oid
    JOIN pg_class child             ON pg_inherits.inhrelid   = child.oid
    JOIN pg_namespace nmsp_parent   ON nmsp_parent.oid  = parent.relnamespace
    JOIN pg_namespace nmsp_child    ON nmsp_child.oid   = child.relnamespace
WHERE parent.relname='parent_table_name';

Use the object identifier type regclass for a very simple query:

SELECT inhrelid::regclass AS child -- optionally cast to text
FROM   pg_catalog.pg_inherits
WHERE  inhparent = 'my_schema.foo'::regclass;

Lists all child tables of given parent table parent_schema.foo. Schema-qualification is optional, the search_path decides visibility if missing.

Similarly, returned table names are schema-qualified and escaped automatically where necessary. Safe, fast and simple.

The solution also works for declarative partitioning in Postgres 10 or later because, quoting the manual:

Individual partitions are linked to the partitioned table with inheritance behind-the-scenes;

Aside, to display the source table for any row retrieved from any table:

SELECT tableoid::regclass AS source, *
FROM   my_schema.foo
WHERE  <some_condition>;