OK, I figured it out so far: I generated a special password and now I am able to send e-mails. But the e-mails have my gmail address as sender instead of the address which I am really using:
----- E-Mail Header ----------------------------------------------------
Return-path: <mygmailaddress@gmail.com>
Received: from mail by mail.lenz-online.de with spam-scanned (Exim 4.92)
(envelope-from <mygmailaddress@gmail.com>)
id 1o6DXj-000C3x-86
for test@test.de; Tue, 28 Jun 2022 17:54:23 +0200
Received: from mail-ed1-f41.google.com ([209.85.208.41])
by mail.mydomain.de with esmtps (TLS1.3:ECDHE_RSA_AES_128_GCM_SHA256:128)
(Exim 4.92)
(envelope-from <mygmailaddress@gmail.com>)
id 1o6DXj-000C3s-5w
for test@test.de; Tue, 28 Jun 2022 17:54:23 +0200
From: My Name <mygmailaddress@gmail.com>
X-Google-Original-From: My Name <myname@mydomain.de>
----- my RoundCube config -------------------------------------------------
$config['smtp_server'] = 'ssl://smtp.gmail.com';
$rcmail_config['mail_domain'] = 'mydomain.de';
$config['smtp_user'] = 'mygmailaddress@gmail.com';
$config['smtp_pass'] = 'abcdefghijklmnop';
Is there a way how to set "myname@mydomain.de" as sender?