- What term describes additional names, such as those added after the middle name?
The name after the first and middle names is usually a surname or family name.
- What term describes surnames which combine two family names, joined by a hyphen?
These are often called double-barrelled names or double-barrelled surnames.
- Are there any additional kinds of names? What are they called?
In much of the west, people usually have at least a first name and a surname. Sometimes they will have one or more middle names.
(There are many cultural exceptions: Hungary has the family name first and the given name last, Portugal with one or two given names and two family names, Iceland is patronymic and sometimes matronymic: the child's surname comes from one of their parent's given name.)
Usually people will be referred to by friends and family by the first name, but occasionally people will go by one of their middle names. This name is used to distinguish them from other people in the same family or with the same surname.
A surname is also known as family name.
The first name is sometimes called a forename and sometimes called a Christian name, whether the person was christened or not. A middle name can also be called these (although first name is usually restricted to the very first one), and in the plural they can refer to the first and middle names together.
A nickname is a shortened version of a given name, or can be a fun or even cruel name to refer to someone more familiarly.
Others end in -onym. For example, a demonym is a resident of a place (eg Mancunian), a fake name or pen name is a pseudonym.
The list goes on and onnic. You can start listing groups of names (eg different types of given names such as Hebrew names, Germanc names, Celtic names), or names of things.