iCloud email alias reveals my full-name when it shouldn't

When using Apple Mail with an iCloud alias email address, my full name is revealed to the receiver of the email, and the alias name is nowhere to be seen. This is a pretty serious security bug and I'm not the only one that is experiencing it.

Steps to reproduce:

I have a main iCloud email address like this:

• johndoe @me.com
• my name connected to it (set in www.icloud.com preferences) is "John Doe"

I created an alias account for forum and spam catching purposes:

• alias @me.com
• my name is set as "Alias Name"

However, when I receive an email to the alias email address and click reply in Mail on my Mac, it suddently adds my full name to the alias email address:

"John Doe" <alias @me.com>

This also happens if an email in the inbox that was sent to the alias email is selected, and I go to compose a new message.

In both cases, from the drop-down in Mail, I can see the following options:

• John Doe <johndoe @me.com>
• Alias Name <alias @me.com>
• John Doe <alias @me.com>

It makes the default one the third one, thus revealing my real name when I don't want it to.

What suggestions do you have for solving this bug?