Yes, I did include an explanation to be on the safe side, the text was:Hi,
I am going through the application process and find myself in the same situation; some of my docs (US docs and my job's reference letter) list only my first last name while others have both (passport, diploma, etc). I am wondering if you ended up adding the clarification letter and if your process went smoothly or you took another approach.
Thanks in advance!
"Because I used to live in the United States and the naming convention in that country is to use the First Name, Middle Name and only one Last Name, some of my personal documents such as my FBI records were generated under that naming convention."