what is it called when you add the sign of a person after a verb to explain a person’s role in asl

The concept you are referring to in American Sign Language (ASL) is called "verb agreement" or "subject-verb agreement." In ASL, many verbs include modifications that incorporate information about the subject or object of the sentence, such as role, location, or direction. This is done by adding specific signs or "inflections" after the verb to convey these details. These inflections can represent the sign for a person (or pronoun) that indicates their role in the sentence, such as the subject or object.