Think about it. When you’re a close friend, you rarely use someone’s full government name. If Leonard said “Penny Hofstadter” every time, it would sound super formal and weird, like a job interview. The show uses this to make us feel like we’re part of their cozy, living-room universe.
It also tells you everything about her role in the group. The boys are defined by their science; they have PhDs and last names that sound like they belong on a library book spine. Penny is the everywoman. She’s not a scientist or a genus of frog; she’s just Penny. Her lack of a surname symbolizes her down-to-earth charm, her normalness in a sea of super-smart weirdos.
Remember how Sheldon never calls anyone by their real name? He doesn’t even use “Penny” most of the time; he just uses her apartment number, “Roommate.” The missing last name is the ultimate sign that she’s beyond labels. She’s the heart, not the footnote.