I'm not super familiar with the history of Mongolia under communism, but it seems a bit counter-productive to eliminate surnames. Since the government was working toward modernizing the country and reforming the society into a communist system, why would they undertake this measure?
The reasoning I've heard is that, due to the surnames (or clan names) being used to identify former nobility and help with clan alliances, they were eliminated to put everyone on an equal footing. Therefore, instead of clan names, patronymics became the new "surname", and is still used today.