Another way is to unite all tables with a union query:
SELECT *, 44 as table_origin FROM `Table_44`
UNION ALL
SELECT *, 58 as table_origin FROM `Table_58`;
You could even prepare that as view:
CREATE VIEW `AllTheTables` AS
SELECT *, 42 as table_origin FROM `Table_42`
UNION ALL
SELECT *, 44 as table_origin FROM `Table_44`
UNION ALL
SELECT *, 58 as table_origin FROM `Table_58`
UNION ALL
SELECT *, 69 as table_origin FROM `Table_69`;
And thus query it safely:
SELECT * FROM AllTheTables WHERE table_origin IN (44,58) AND something = 'foobar';
-- or --
SELECT * FROM AllTheTables WHERE table_origin = 42 AND something = 'the question';
In your exact case it could look like this:
SELECT var1, var2, var3, table_name
FROM table1 LEFT JOIN AllTheTables ON table1.var3=AllTheTables.table_origin