Det er stort set alt hvad du behøver:
mysql> select * from t;
+------+-------+
| id | data |
+------+-------+
| 1 | max |
| 2 | linda |
| 3 | sam |
| 4 | henry |
+------+-------+
4 rows in set (0.02 sec)
mysql> update t set data=concat(data, 'a');
Query OK, 4 rows affected (0.01 sec)
Rows matched: 4 Changed: 4 Warnings: 0
mysql> select * from t;
+------+--------+
| id | data |
+------+--------+
| 1 | maxa |
| 2 | lindaa |
| 3 | sama |
| 4 | henrya |
+------+--------+
4 rows in set (0.00 sec)
Ikke sikker på, hvorfor du skulle have problemer, selvom jeg tester dette på 5.1.41