What you need is a correlated subquery with a group by.
One way to do this which is easy to follow is:
SELECT column1, name, column2
FROM MyTable as mt1
WHERE column1 in (SELECT Min(column1) FROM MyTable as mt2 GROUP BY column2)
But a better, cleaner way:
SELECT column1, name, column2
FROM MyTable as mt1
INNER JOIN
(SELECT Min(column1) as minc1 FROM MyTable as mt2 GROUP BY column2) as mt2
ON mt1.column1=mt2.minc1;
Note: These two forms should be supported by most DBMS's.