It's difficult to definitively say which country has only first names, as naming conventions vary widely and can be complex. However, several countries have cultural practices where individuals commonly use only a single name, often a given name.
For example, in Indonesia, especially on the island of Java, many people have only one name. Traditionally, commoners had a single name, while nobles often used multiple names. In this context, it's more about the social and historical context rather than a strict legal rule.
While it's not accurate to say that any country exclusively uses first names, certain cultures have a strong tradition of using a single, given name, making it seem like they have "only" first names.