A user whose access is limited by section should see only students in their own section in the People tool's group tabs. Only the Everyone tab in the People tool respects section-limited access, at this time. A user whose access is limited to their section can see the group memberships, and therefore the names, of students belonging to other sections under the People tool’s groups tabs. Hiding the People tool is an effective (but undesirable) workaround to limit student access, but it does not limit access for Teachers, TAs, or Designers.
For reference, How do I limit a user to only interact with other users in the same course section? lists People as one of the tools affected by section-limited access.