Do people in Mongolia have just one name?

Mongolians don't have a system of surnames equivalent to English or Chinese family names. I gather that people mainly use their first name but officially will have their father's name before it to distinguish between people with the same name. Since 2000 they have also used 'clan' names (sometimes made up) though the Chinese bureaucracy doesn't recognise these clan names. It's very confusing.

https://en.wikipedia.org/wiki/Mongolian_name

As far as I remember, the Mongolian leader Choibalsan (a firm Stalinist) was known by only this name. But now I see in the Wiki page that he has two names.

https://en.wikipedia.org/wiki/Khorloogiin_Choibalsan

By the way, there may be a different situation in Inner Mongolia (belongs to China) and Outer Mongolia (which is the republic of Mongolia).

'As part of restoring their national identity, people started to search for their roots and in 1991 President P. Ochirbat issued a decree for the restoration of family names. People were free to pick their own names, ' said Serjee who has written a guide on how to do it. Most people have chosen the Genghis Khan family name, Borjigid, which like many other names is taken from clan totem.

Other Mongolians are named after other animals like eagles or crows, as well as professions such as smith, hunter, or camelbreeder.

Although 60 percent of Mongolians have preferred to choose to belong to Genghis Kan's clan, others have sought to found their own illustrious name like, Mongolia's first and so far only man in space. Cosmonaut Gurragchaa, who returned to earth in 1981, has registered himself as Mr. Cosmos, ensuring that generations to come will not forget who they are and where they came from.

https://archive.li/r6yCQ#selection-447.6-447.193
mongoliatoday.com/issue/5/names.html no longer exists