This site will answer all the frequently asked questions by IMGs about preparation for the USMLEs and Residency. On the right side you will find the categories list where you will find the questions and answers for each category.
Do I need my AAMC ID or USMLE ID on the LOR?
Many people when it come to upload letters of recommendations they get stuck with this query, should I write my AAMC ID or USMLE ID on the LORs?
Actually neither of them is required because you are uploading it yourself and so it will go directly to your account. Program directors will not worry about who's LOR is this. Even if it is waived and the writer is uploading it for you, the request you print from your MyERAS is unique for you and it have the sufficient security information that will send the LOR only to your application.
If you still obsessive about it, then don't worry, just write one or both of them down with your hand on one of the corners of the letter and this is completely acceptable and fine.