Generally speaking, foreigners have three names, which are called first name, middle name and last name in English. This first name is what we usually say, and last name is the surname. However, foreigners have a habit that when parents name their children, they will use the names of people they respect, or the names of grandparents, which means that the characters in middle name and China's name are similar in nature.
As the landlord said, we generally don't call this middle name or word. Its function is only to show respect for the elders or as a way to commemorate the respected people.
I don't understand what the landlord means by the primary name and the secondary name, but although foreigners do have two names, they only have the first name, that is, the name written in front of them.
I hope it helps you ~
Heaven ~