The support system merely takes the first part of your email address (everything before the @) and uses it as a name when automatically creating the contact upon receipt of your first email. It is not integrated with our network and does not attempt to determine what your actual display name is on-site.
Since we don't allow end-users to login to the support system itself, it's also not possible for the name to be changed after the initial contact has been created without us having to go manually change it. So attempting to fetch "current display name" is probably not a great idea anyways - it will just become wrong again the moment you change it.
We previously did not include the user's "name" in the reply, because they were frequently gibberish and meaningless. Think of the people who use things like firstname.lastname@example.org and us sending a message that says "Hi stackoverflow" - weird.
But, users who do email us directly (not via the contact form) have the name populated properly with what was is sent in via the email headers. Direct email is more common among our paid products, where addressing the user by name in a reply is a common courtesy and helps personalize the email, which is why it was turned on. Unfortunately we cannot turn it on/off selectively based on the type of support request.