You can at least workaround this problem by using Settings/Identities (third tab from the left) and checking the "Set default" checkbox.

I can't tell why and where the address "no-reply@hollozoltan.extra.hu" is created from.

Jonathan Nichols wrote:

...

But my webmail client use this e-mail address: no-reply@hollozoltan.extra.hu instead of my default e-mail address: hollozoltan@extra.hu

In which configuration file can I modify this settings?

That almost sounds like a MTA issue. Something like sendmail or Postfix.

Yes, I assume the same. You most likely don't have an SMTP server configured in Roundcube and in this case it uses PHP's built in mail() function to send mails.

I recommend to configure 'smtp_server' and other SMTP related properties in Roundcube's config/main.inc.php file in order to make Roundcube talk directly to an SMTP server when sending mails.

~Thomas