This is a very important consideration.

The are discussions where user name matters, for instance when refering to the nth parent in the same thread, or when trying to bring more context to a point made previously or even retracting a comment (knowing it's the same user posting is important).

We could get away with temporary user names, changing on a per thread basis for instance, but that might be heavy to implement.

>for instance when refering to the nth parent in the same thread

waterlesscloud's suggestion is to hide them only while the comment is pending. Once the comment is approved, then the username can be displayed as normal, allowing references.

Apply the on first participation to the thread then ?

Or just copy 4chan's system directly, since that's what you're iterating towards, and they've already solved this problem.