There is no need for a trigger or something else. This is the key to a relational database design.

The value (of VENDOR_NAME) is stated on one position and is displayed on all locations with the use of key-references. With a SELECT statement you join the two tables together on the key reference (VENDOR_ID).

You can use the code below to display the joined data of both tables:

SELECT

SYSTEM_ID

, SYSTEM_NAME

, table1.VENDOR_ID

, VENDOR_NAME

FROM table1

INNER JOIN table2

ON table1.VENDOR_ID = table2.VENDOR_ID

You can update the VENDOR_NAME with statement:

UPDATE table2 SET VENDOR_NAME = 'new_name' WHERE VENDOR_NAME = '{existing name}'

If you execute the SELECT statement before and after the UPDATE, you can see the SELECT will always return the actual values.