It’s great,
when I am quoting, the login name is embedded intead the display name. Also when answer to a post, on the bottom there is window showing the thread. In this window also the login names are shown instead of the display name.
What is the difference for, if it does not work?
For secret reasons the login name should never show!
What’s the problem with it, is one less “secret” then the other ?
Then please tell me, what is the login name for and what is the display name for?
You’d have to ask the phpBB programmers, follow the link at the bottom of the page 
It seems to be a problem of this installation. See phpBB • Displaying a Display Name instead of a user name
… which doesn’t present a “solution”
but then can you tell me a way to change my login name to my display name and also can you tell me the reason, why you decided to use the display name mod of phpBB?
Other forums also use display name and login name and always show display name and never show the login name for privacy reasons!
I’m just a regular forum user and not the administrator, so I can’t tell you.
I assume you’ll have to re-register with a very, very “secret” login name equalling the display name.