For instance, say I have two individuals and one is active, the other passive. I know I can call the active person the "actor"—he "acts upon" the passive person. But what do I call the "acted upon"? Is there a single word to describe this?
The term is Patient, which is formed from the same semi-deponent Latin verb (patior, patere, passus 'suffer, endure') as Passive. Most grammatical terminology comes from Latin, so if you want to make up a linguistic term, get a Latin dictionary.
In a prototypical English active transitive sentence,
- the grammatical relation Subject has a semantic role Agent (< ago, agere, egi, actus 'do'),
- the grammatical relation Direct Object as the semantic role of Patient.
In Functional Grammar the person or thing acted upon is the Patient.
This may seem an odd use of the word, but it is not, in fact, a coinage of modern linguistics. Patiens (the present participle of pati, “to undergo, endure, suffer”) and agens were literal Latin translations of Aristotle’s terms, and the opposition has been used in English since the 16th century:
The eye of the man is the arrow, the bewtie of the woman the white, which shooteth not but receiueth, being the patient, not the agent. —Lyly, Euphues 1580
Love or hate, applaud or condemn, the agents and the patients of [Shakespeare's] mundane scheme. —Swinburne, Essays & Studies 1875
In some circumstances, the term object can be used, as in
She was the object of his affections.
Cambridge defines it as
the particular person or thing to which others direct thoughts, feelings, or actions: The court has been the object of recent criticism
Somewhat ironically, the term subject may also be used. Definition 5 in American Heritage says
One that experiences or is subjected to something: the subject of ridicule.
A person or animal that is the object of medical or scientific study: The experiment involved 12 subjects.
A corpse intended for anatomical study and dissection.
One who is under surveillance: The subject was observed leaving the scene of the murder.
Actor is a term used in functional grammar to describe the person or thing that initiates a material Process (but not other kinds of Process), that is, some kind of action that takes place in the real world. If you want to be consistent with the use of Actor in functional grammar, then the term to use for the person or thing on the receiving end is the Goal (not, pace John Lawler and StoneyB, the Patient). In a mental Process it is the Phenomenon, in a Relational Process, the Value, and in a Verbal process, the Verbiage.
FWIW, in various computing process models I've constructed that have an Actor role, the role of that which is acted upon has been either a Subject or a Target.