Sometimes you discover someone in your head who does not tell you their name right off the bat. Short of referring to them as "that new person" and "hey you!", often you want to give them a name so that you can deal with them in a civil fashion.
Many books on multiples show that residents can be named after their function. There's a distinct disadvantage to naming someone after their function, because firstly it is generally very limiting to think that the most notable function you're aware of is not always the full extent of noteworthy functions a resident has, and because the function can change over time, and then you're stuck having to deal with renaming a resident, and you have all the same problems of finding a name for them that you had in the first place. Another possible problem is that when "the Angry One" is attempting to get over being so angry, the name itself might become a hinderance.
So, you might wish to make up a name, or tackle a baby book, or alter a function name so that it's not really a function name at all (For example, The Crisses took "shame", a notable trait of someone in their head, and named the person Shane).