Upvote:2
You will not need a passport of any form of ID to buy a prepaid SIM card in Ulan Bator.
You can purchase a SIM card on the third floor of the Seoul Business Center just across the street from the Chinggis Khan Hotel. I felt like I was applying for a loan (small, private office; person doing the sale spent a lot of time typing in a computer). However, their English was good enough to answer my questions.
They said it would take 30 minutes for the SIM to be activated. I had to go back and have them add some information to my phone to make data work.
I paid in cash. 8,000 Tugriks (~$5.25) gets the SIM and some credit. It seems like telecommunications prices are low in Mongolia.