Setting A Colliding Object as "Selected Object"

Well, you can also do it this way. To change an object variable in object B, in the object A trigger machine, just add in the change variable node, set variable origin to Object, type in the variable you want to change into the variable key, and in the object section, just put in starting object.
The starting object is whatever object that collides with object A. So whether it's object B or Z, the moment it collides with object A, that object will be the starting object. Of course, the limitation of such method you want is that all object variables of the gameobject A to Z must have the same object variable name.

If they are different, you will have to do it the long way, and in the object A trigger machine, you will have to add in the check object name node, and changing their respective object variables upon success.

Generally, the Machine Object is the game object the machine is running on (usually where the component is added to), the starting object is the one that started the machine, e.g. through colliding with the machine object or interacting with it.
Since interactions can only be caused by the player, the starting object of an interaction machine is usually the player's game object.

For your desired setup, using what @Shadow_Fire explained should be enough. For anything more complex, e.g. each object playing different animations or spawning prefabs or whatever, you'll have to use trigger machines on those game objects.