so resuming (as you'll have understand i can't focus well the thing):
The Main Username doesn't allow Underscore like "antoine_4"
where? seem in wp you can use it. So i assume In buddypress maybe no?
Because of the previous problem, the rightfull username is on the "name" section and not the "username" section in the registration.
But in WP, in phpBB, only the main username is displayed !
Only the main username, because phpBB not provide a custom name to use in place of username (or i'm wrong?) . So to get this result...
You want WP custom name, display for users in members list of phpBB or as username in phpBB on any phpBB contest?
Thinking better on it and how should done, included into this plugin maybe.
Add a custom phpBB profile field for user (can be created also via phpBB ACP admin): this field on db, will be filled by the plugin code with WP display name, and also maybe something custom until user not choose to setup the custom display_name on wp or phpBB profile.
So in phpBB, as above mentioned, it is needed just a function that switch to display the custom display_name in place of username, because due to the above at this point this data is available value to display into phpBB.
This should be the complete, correct easy joke.
p.s ways to achieve the result are several, it depend by the needed result to choose the best route.
I will follow with this about custom profile fields, and buddypress ...