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".
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.