Update row with data from another row in the same table

Try this:

UPDATE data_table t, (SELECT DISTINCT ID, NAME, VALUE
                        FROM data_table
                       WHERE VALUE IS NOT NULL AND VALUE != '') t1
   SET t.VALUE = t1.VALUE
 WHERE t.ID = t1.ID
   AND t.NAME = t1.NAME

Here's my go:

UPDATE test as t1 
    INNER JOIN test as t2 ON 
        t1.NAME = t2.NAME AND 
        t2.value IS NOT NULL 
SET t1.VALUE = t2.VALUE;

EDIT: Removed superfluous t1.id != t2.id condition.