Welcome to the community.
It is certainly possible to adjust the formatting of the 'Appointment' letter tag results.
Most users will either be using the <<NextAppointment>> letter tag, or the <<AppointmentTime>> tag (recommended). The AppointmentTime tag is a newer addition to Front Desk, and is recommended as it will produce more accurate results when a patient has several appointments on the same day.
To change the date formatting, all you need to do is add the required format in brackets at the end of the letter tag. This is very flexible, as the following examples show:
<<AppointmentTime(dd/mm/yyyy h:nnam/pm)>> will give you "11/06/2015 3:00pm"
<<AppointmentTime(dddd d/m "at" h:nn am/pm)>> will give you "Thursday 11/6 at 3:00 pm"
<<AppointmentTime(ddd d/m "at" hh:nn)>> will give you "Thu 11/6 at 15:00"