abap program for FM to Get the Day for a Particular Date

FM or any other means by which we can get the DAY for a particular date?

Yes, DATE_COMPUTE_DAY

Sample code:

clear: hold_day_of_week.

CALL FUNCTION 'DATE_COMPUTE_DAY'
EXPORTING
DATE = workdate
IMPORTING
DAY = day_of_week_num
EXCEPTIONS
OTHERS = 8.

CASE day_of_week_num.
WHEN 1.
hold_day_of_week = 'Monday'.
WHEN 2.
hold_day_of_week = 'Tuesday'.
WHEN 3.
hold_day_of_week = 'Wednesday'.
WHEN 4.
hold_day_of_week = 'Thursday'.
WHEN 5.
hold_day_of_week = 'Friday'.
WHEN 6.
hold_day_of_week = 'Saturday'.
WHEN 7.
hold_day_of_week = 'Sunday'.
WHEN OTHERS.
hold_day_of_week = 'invalid'.
ENDCASE.

or

You can use DATE_COMPUTE_DAY to get the day number of the week (for example, today gives 5)
then use WEEKDAY_GET which returns an itab with seven entries (one for each day of the week.)
You enter in this itab and get the field langt to get the day name.