Here's the easy way:
SELECT
t.login_name
,COUNT(t.id) AS login_counts
,MAX(t.login_time) AS latest_login_time
FROM this_table AS t
GROUP BY t.login_name
ORDER BY login_counts DESC, login_name
;
The top line gives you the login_name
with the most logins.
And here's the hard way:
SELECT
t.login_name
,MAX(t.login_time) AS latest_login_time
FROM this_table AS t
INNER JOIN (
-- Determine who has the most logins
SELECT TOP 1 x.login_name, COUNT(x.id) AS login_count
FROM this_table AS x
GROUP BY x.login_name
ORDER BY login_count DESC -- to get the highest counts first
) AS m
ON t.login_name = m.login_name
GROUP BY t.login_name
;
That gets you one name and date, and that's it, though it doesn't take into account the possibility that there could be more than 1 name with the maximum number of logins. I'll leave that up to you to figure out.