It may be against Facebook's TOS to use a fake name but you can definitely get away with it. However, if you are adding friends and family to your list of facebook friends then it might not be hard at all to figure your real name out.
Please let's not use 'allowed to use a pseudonym' and 'wants to hide his real name' interchangeably.
If you want to/have to hide your real name, a pseudonym might help (and your suggestion is helpful). But not everyone using a pseudonym tries desperately to hide his real name.
Nothing against your post, I just want to make a case for pseudonyms while avoiding to reduce this to 'some people are in real danger of violence' cases etc.
Let people choose their names. Regardless of their motivation.
* Pseudonym: An identifier of a subject other than one of the subject's real names.
* Real name: The opposite of a pseudonym. For example, [...]
* Pseudonymous: A property of a data subject in which the subject is identified by a pseudonym.
* Pseudonymity: The state of being pseudonymous.
Pseudonymity is strengthened when less personal data can be linked to the pseudonym; when the same pseudonym is used less often and across fewer contexts; and when independently chosen pseudonyms are more
frequently used for new actions (making them, from an observer's or attacker's perspective, unlinkable).
So according to these definitions, you're right that a pseudonym by itself may not require one to conceal their "real" identity. However, pseudonymity clearly does.
I think pseudonymity is the more fundamental as a general security property. So your example of a person using a pseudonym without significant desire for pseudonymity is more of a corner case, at least in serious discussions.
If we need a term for a pseudonym without strong pseudonymity, I propose we use the term from IRC and call it a "nick".
Family maybe, but figuring out the real name from friends can get difficult.
I know a guy who has been using an alias on facebook for the past 8 years or so. It is funny to watch when his alias creeps in to real life. Normal scenario, Bob meets Alice, a friend of a friend, at a party. They friend each other on facebook, Bob uses the alias Claude. Sometime passes and they run into each other elsewhere. Since Alice met many people that day and now mostly only remembers Bob as Claude from facebook. Some confusion occurs when Bob's friends call him Bob while Alice is convinced his name is Claude.
This happens to me a lot. I don't think Facebook are even interested in enforcing real names though, my middle name is currently "Hashtag", it is obvious that it is not a real name yet it was accepted.
That reminds me of a site that, in protest to arguments made for criminal hacking charges in the "MySpace suicide" case, changed its TOS to ban people named "Steve" from visiting at all.
I hope that we make more headway, in the legal and popular understanding, that website TOSs currently seem to amount to nothing more binding than "No Shirt, No Shoes, No Service" signs.