yeah syntax is important here;

you already identified that you know the a trigger should refer to the virtual inserted or deleted tables;

the key is that the original table needs to join to inserted and/or deleted in order to properly update/

most likely, what you want is this inside your trigger

CREATE TRIGGER TR_Test_IU ON Test

FOR INSERT,UPDATE

AS

BEGIN

UPDATE MyTarget

set MyTarget.Name='DIT'

FROM Test MyTarget

INNER JOIN INSERTED

ON Test.ID = INSERTED.ID

WHERE name='D'

END --TRIGGER