Final answer:
Erving Goffman's concept of the degree to which an individual embraces a role is known as his theory of dramaturgy, where individuals adjust their behavior and presentation based on the social context they are in.
Step-by-step explanation:
Erving Goffman's concept of the degree to which an individual embraces a role is known as his theory of dramaturgy. Goffman proposed that individuals perform different roles depending on the situation they are in, similar to actors on a stage. He believed that people use impression management to present themselves to others as they hope to be perceived. This theory suggests that individuals adjust their behavior and presentation depending on who is present and the social context they are in.