You should be fine at Medpark.
I got my 1st AZ on 12 July at Medpark.
Received my 2nd shot yesterday - no problem (was a week or so earlier than originally booked due to work commitments meant being away from Bangkok at that original time).
Got the A4 vaccine certificate after the 30 minute wait - they did ask for my passport number also to add into the system (I was booked using my pink ID card number). My passport number was entered and a couple of hours later I checked on the Mor Phrom App, and the Vaccine Certificate is there, as is a Digital Health Pass which has my passport number and vaccination status (my name is written in Thai on this Health pass, in English on the vaccine certificate).
I've taken screen shots and saved to Notes on my phone just in case of App issues or not having any internet connection when needed.
