Get the name of a row's source table when querying the parent it inherits from

To identify the source table of a particular row, use the tableoid, like you found yourself already.
A cast to regclass retrieves the actual name, automatically schema-qualified where needed according to the current search_path.

SELECT *, tableoid::regclass::text AS table_name
FROM   master.tbl
WHERE  <some_condition>;

More:

• Find out which schema based on table values
• Select (retrieve) all records from multiple schemas using Postgres
• How does the search_path influence identifier resolution and the "current schema"