Can people refer to me as an MD in my recommendation letter if I have already passed my professional exam but my degree is still in process? This year I am applying to an big university's summer camp this year, and I am not really aware of how US Universities handle this situation. I am a Mexican "medical intern", I call myself like that because I know no better term to describe my degree, which would be literally translated as "In-Social Service Medical Doctor". I have already taken and passed my professional exam, but my degree is still in process, and probably (very likely) won't be ready at the submission of my papers. 

If it were a Mexican institution I would just use "MPSS" (Medical Intern at Social Service by Spanish acronym). However medical intern seems like I have just finished medical school and I am at my Internship year (which it not the case, I have already finished it, thanks god).

The only question I have is: would it be recommended that my teachers to refer to me as INSTERT FULL NAME HERE M.D. or Dr. INTERT FULL NAME in my recommendation letters? if it is not, how could they call me in those letters?
I am struggling to understand exactly the position you are applying for and don't know much about the medical field, but would expect your references to refer to you on a first name basis in the letter. This seems even more likely in the case where the degree status is in flux/unclear. At some point in the letter it should probably say something like


  Luis has completed their MPSS at University of Mexico, completed the internship year, and passed their professional exam. They have completed all the requirements for their doctorate in medicine and will be receiving the MD degree at the graduation ceremony in May.