Просто соедините все три таблицы.
SELECT concat(p.person_fname, ' ', p.person_sname) `Person`,
a.appointment_type `Appointment Type`,
a.appointment_date `Appointment Date`
FROM person p
INNER JOIN personappointment pa
ON pa.person_id = p.person_id
INNER JOIN appointment a
ON a.appointment_id = pa.appointment_id;