Name EmpName Date
 -----------------------
 abc   emp1   3/19/2018
 abc   emp1   3/22/2018  (This record should be rejected)
 xyz   emp2   3/15/2018   valid record

SELECT
    name, empname,
    ROW_NUMBER() OVER (PARTITION BY YEAR(date), MONTH(date) ORDER BY date DESC)

select top (1) with ties t.*
from table t
order by row_number() over (partition by name, empname, year(date), month(date) order by date);

select name, empname, min(date)
from table t
group by name, empname, year(date), month(date);