Don't think there is a built-in way of doing this, in the past I have either popped the call stack or used DBMS_ROWID with the ROWID of a row, example follows...
Code:
Oracle9i Enterprise Edition Release 9.2.0.4.0 - 64bit Production
With the Partitioning, OLAP and Oracle Data Mining options
JServer Release 9.2.0.4.0 - Production
SQL> CREATE TABLE table_name (column_name NUMBER);
Table created.
SQL>
SQL> CREATE FUNCTION object_name (
2 p_rowid IN ROWID)
3 RETURN all_objects.object_name%TYPE
4 IS
5 v_object_name all_objects.object_name%TYPE;
6 v_object_id all_objects.object_id%TYPE;
7 BEGIN
8 v_object_id := DBMS_ROWID.ROWID_OBJECT (p_rowid);
9
10 SELECT object_name
11 INTO v_object_name
12 FROM all_objects
13 WHERE object_id = v_object_id;
14
15 RETURN v_object_name;
16 END;
17 /
Function created.
SQL>
SQL> CREATE TRIGGER trigger_name
2 AFTER INSERT
3 ON table_name
4 FOR EACH ROW
5 BEGIN
6 DBMS_OUTPUT.put_line (object_name (:NEW.ROWID));
7 END;
8 /
Trigger created.
SQL> SET SERVEROUTPUT ON;
SQL> INSERT INTO table_name VALUES (1);
TABLE_NAME
1 row created.
SQL>