The way to do this is to use a FULL OUTER JOIN, but since this is not supported in MySQL you can instead use a combination of a LEFT JOIN and INNER JOIN and RIGHT JOIN.
(
SELECT A.Id, A.Name, 'A' AS Found
FROM A LEFT JOIN B ON A.Name = B.Name
WHERE B.Name IS NULL
)
UNION ALL
(
SELECT B.Id, B.Name, 'B' AS Found
FROM A RIGHT JOIN B ON A.Name = B.Name
WHERE A.Name IS NULL
)
UNION ALL
(
SELECT A.Id, A.Name, 'C' AS Found
FROM A JOIN B ON A.Name = B.Name
)
In fact, you only need a LEFT and RIGHT JOIN because you can handle the INNER JOIN at the same time as you do one of the other two joins. I think the above demonstrates the principle more clearly, but in practice the following will give better performance:
SELECT A.Id, A.Name, IF(B.Name IS NULL, 'A', 'C') AS Found
FROM A LEFT JOIN B ON A.Name = B.Name
UNION ALL
SELECT B.Id, B.Name, 'B' AS Found
FROM A RIGHT JOIN B ON A.Name = B.Name
WHERE A.Name IS NULL
Result:
Id Name Found
1 Scott A
2 Dan C
3 Sam A
2 Andi B
3 Jess B