Update with two tables?

Your query does not work because you have no FROM clause that specifies the tables you are aliasing via A/B.

Please try using the following:

UPDATE A
    SET A.NAME = B.NAME
FROM TableNameA A, TableNameB B
WHERE A.ID = B.ID

Personally I prefer to use more explicit join syntax for clarity i.e.

UPDATE A
    SET A.NAME = B.NAME
FROM TableNameA A
    INNER JOIN TableName B ON 
        A.ID = B.ID