Hi Tom - First of all, I would like to Thank you for all the time to invest to answer our questions. It is always insightful to read (and understand) your answers :)

Though I have asked this question in other forums, I have not satisfied with the responses, so I am asking you.
---------------

I have seen and used many times, "Date" column (some times, just the date, and some times, Date along with time component) as part of the primary key.

I want to maintain a primary key, that contains a set of columns along with a date range (duration) of time between two date columns, so there will be no duplicate records for the ENTIRE RANGE of Start and end dates.

Here is the process I followed, however I know there can be better ways to do this... Please share it if you can..
My question is - is there any easier/better/organized way to implement this??

Here is my way
---------------
Lets say I want to create a table that maintains the "name changes for a given person over a period of time".
To achieve that I have two tables listed below.

1. This maintain list of ALL person_IDs.

CREATE TABLE person_ids (person_id NUMBER CONSTRAINT person_id_pk PRIMARY KEY);

2. For each person listed in the above table, we want to maintain legal_name over different periods of time.
In this below table

CREATE TABLE person_m
(
 rec_id                        NUMBER CONSTRAINT person_m_pk PRIMARY KEY
,person_id                     NUMBER CONSTRAINT person_m_fk1 REFERENCES person_ids(person_id)
,legal_name                    VARCHAR2(32)
,eff_from_ge_dtm               DATE
,eff_thru_lt_dtm               DATE
,CONSTRAINT person_m_fk2 CHECK(eff_from_ge_dtm <= eff_thru_lt_dtm)
);

Just to make sure, I relay the meaning of the column names.
rec_id is a "surrogate key", no importance for it.
eff_from_ge_dtm - Effective from (greater than or equal to) this specific date&time.
eff_thru_lt_dtm - The legal name is effective until (but less than) this specific date&time.

I want to make sure the uniqueness of a person_id and duration between eff_from_ge_dtm, and eff_thru_lt_dtm.

INSERT INTO person_ids VALUES(1);

INSERT INTO person_m VALUES (1001, 1, 'LN1', TO_DATE('2001/01/01','yyyy/mm/dd'), TO_DATE('2010/01/01','yyyy/mm/dd'));
INSERT INTO person_m VALUES (1002, 1, 'LN2', TO_DATE('2010/01/01','yyyy/mm/dd'), TO_DATE('2012/01/01','yyyy/mm/dd'));

For the same person identified by "1", we have two names for the given two different date&time ranges.
We can not have overlapped date range records for a given person.

For that I have created a function that checks if the incoming record values cause any overlaps and returns a Yes OR No.
I call this in a trigger (or in a another procedure) where the actual insert is going to happen.

CREATE OR REPLACE FUNCTION does_cause_overlap_dt_range_yn(
                                          i_person_id                 IN NUMBER
                                         ,i_lower_date_val            IN DATE
                                         ,i_upper_date_val            IN DATE)
    RETURN VARCHAR2 IS
    l_yes_no                      VARCHAR2(1);
    l_cnt                         NUMBER;
  BEGIN
    BEGIN
      SELECT 1
      INTO  l_cnt
      FROM  person_m e1
      WHERE e1.person_id = i_person_id
        AND   NOT (   e1.eff_from_ge_dtm >= ALL (i_lower_date_val, i_upper_date_val)
                   OR e1.eff_thru_lt_dtm < ALL (i_lower_date_val, i_upper_date_val)
                  );
      -- if there is one record, that means it is going to cause overlap           
      l_yes_no                   := 'Y';
    EXCEPTION
      WHEN NO_DATA_FOUND THEN
      -- no overlaps
        l_yes_no                   := 'N';
      WHEN TOO_MANY_ROWS THEN
      -- overlaps
        l_yes_no                   := 'Y';
    END;
    RETURN l_yes_no;
  END;