Since you did not mention any RDBMS, this query will work on almost all RDBMS.
SELECT a.*
FROM TableName a
INNER JOIN
(
SELECT Name, MAX(Year) Year
FROM TableName
GROUP BY Name
) b ON a.Name = b.Name
AND a.Year = b.Year
However, if your RDBMS supports window functions, you can use ROW_NUMBER()
SELECT Year, User_ID, Name
FROM
(
SELECT Year, User_ID, Name,
ROW_NUMBER() OVER (PARTITION BY Name,
ORDER BY Year DESC) rn
FROM TableName
) x
WHERE x.rn = 1