when I applied for dental treatment, UK embassy required letter and addressed to thai embassy and signed by authorised person. As long as it is signed, this should be more than enough.
It states on thai embassy website, you need a letter of confirmation of appointment and treatment. it needs to be on letterhead paper addressed to the thai embassy of where you are applying, and signed by an authorised person. Hope this helps
For me dentist will have 2 appointments. This is also from UK - I would email your thai embassy for your country. Another guy from uk only has only one appointment.