Apply group by having order by with latest record

You can use window functions in the order by. But you probably also want to keep the names together when there are ties, so you need three keys:

order by max(date) over (partition by name) desc,
         name,
         date desc;

Note that you can also use other tie breakers. For instance, when two names have the same most recent date, you can put the one with the most recent earliest date first with an additional key:

order by max(date) over (partition by name) desc,
         min(date) over (partition by name) desc,
         name,
         date desc;

I guess you're looking for

WITH CTE AS
(
  SELECT *, ROW_NUMBER() OVER(PARTITION BY Status ORDER BY [Date]) RN
  FROM
  (
    VALUES
    ('john', 'print', '2020-07-24'),
    ('john', 'read', '2020-07-23'),
    ('matt', 'print', '2020-07-24'),
    ('matt', 'read', '2020-07-23')
  ) T(Name, Status, [Date])
)
SELECT Name, Status, [Date]
FROM CTE
ORDER BY RN DESC;

Here is a db<>fiddle

You can use window functions:

select *
from mytable t
order by max(date) over(partition by name) desc, date desc