Check out the "Category" thing in "Contact details." You can edit the ones that are already there (the documentation says it's best to keep the meaning consistent with the original intent), and you can also add your own.
If the "category" thing isn't what you want, you can make a user defined field. But it's usually best to use the built-in field for something, since it's going to take up space on your screen. Having too many user-defined fields is a pain.