Find max date record from multiple columns and with null

The following query will give you the expected output for your sample input:

WITH cte As
(
    SELECT
        EmpID,
        Name,
        Date1,
        ROW_NUMBER() OVER (PARTITION BY EmpID ORDER BY Date2 DESC) As RN
    FROM
        YourTable
)
SELECT
    EmpID,
    Name,
    Date1
FROM
    cte
WHERE
    RN = 1
;

Output:

EmpID | Name | Date1
=========================
    1 |    A | 2021-01-30
    2 |    B | NULL
    3 |    C | 2021-01-28

However, you mention that you've already done something like that "for one date only".

But you haven't explained what is wrong with that output.

ROW_NUMBER() OVER (PARTITION BY EmpID ORDER BY Date2 DESC, Date1 DESC) As RN

Not sure if I understand the requirement correctly but from what I gather you first need to find the rows for each empid containing max based on date2 and then from this set the rows having max of date1 per each empid.

If this was correct interpretation, you could consider something like this
First the example data

create table ta1 (
   empid int,
   name  varchar(10),
   date1 date,
   date2 date
);

insert into ta1 (EmpID, Name, Date1, Date2) values 
(1, 'A', '30/Jan/2021', '20/Jan/2021'),
(1, 'A', '29/Jan/2021', '20/Jan/2021'),
(2, 'B', Null,          '20/Jan/2021'),
(2, 'B', NUll,          '21/Jan/2021'),
(3, 'C', '28/Jan/2021', '21/Jan/2021');

Now let's get the rows having max date2 for each emp. The query could look like this

WITH Date2Query AS (
   SELECT t1.empid, 
          t1.name, 
		  t1.date1,
		  t1.date2
   FROM ta1 T1
   WHERE t1.date2 = (select max(t2.date2) 
                     from ta1 T2 
					 where t1.name = t2.name)
)
SELECT * FROM Date2Query;

so the result would be

empid name date1      date2
3     C    2021-01-28 2021-01-21
2     B    NULL	      2021-01-21
1     A    2021-01-30 2021-01-20
1     A    2021-01-29 2021-01-20

Now to get the rows for each emp having max of date1 you can use the approach you already tried but in case of null, use a non-existent date in the comparison to ensure that if max is null then the comparison is true. For example using COALESCE the query could look like this

WITH Date2Query AS (
   SELECT t1.empid, 
          t1.name, 
		  t1.date1,
		  t1.date2
   FROM  ta1 T1
   WHERE t1.date2 = (SELECT max(t2.date2) 
                     from ta1 T2 
					 where t1.name = t2.name)
)
SELECT t1.empid, 
       t1.name, 
       t1.date1
FROM Date2Query T1
WHERE COALESCE(t1.date1,'01/01/1900') 
      = COALESCE((SELECT MAX(t2.date1) 
                  FROM Date2Query T2 
				  WHERE t1.name = t2.name),'01/01/1900') ;

And the result is

empid name date1
3     C    2021-01-28
2     B    NULL
1     A    2021-01-30

This can be re-written in several ways. One option is to fetch NULL's and non-NULL's separately, for example

WITH Date2Query AS (
   SELECT t1.empid, 
          t1.name, 
		  t1.date1,
		  t1.date2
   FROM  ta1 T1
   WHERE t1.date2 = (SELECT max(t2.date2) 
                     from ta1 T2 
					 where t1.name = t2.name)
)
SELECT t1.empid, 
       t1.name, 
       t1.date1
FROM Date2Query T1
WHERE t1.date1 = (SELECT MAX(t2.date1) 
                  FROM Date2Query T2 
				  WHERE t1.name = t2.name)
UNION ALL
SELECT t1.empid, 
       t1.name, 
       t1.date1
FROM Date2Query T1
WHERE t1.date1 IS NULL;