Your name: John Doe (My Company Name)
Mail address: info@mydomain.com
Reply-To: info@mydomain.com
Outgoing server: Use Standard Server

Google Mail: smtp.gmail.com (Standard)
Description: Google Mail
Server: smtp.gmail.com
Port: 465
User Name: johndoe@gmail.com
Authentification: Password, normal
Connection Security: SSL/TLS

From: John Doe (My Company Name) <johndoe@googlemail.com> (<-- this is wrong)
Subject: Some Test Mail to check my name
Reply To: Me <info@mydomain.com>