So you logged into webmail as admin, sent an email as admin, and then complain when admin shows up in the header.
Don't login as admin. You have to first create the email address you want to use. Then login as that virtual email user. Then send your email.
You can also create multiple identities in the webmail program.
You are not having a DirectAdmin problem. The problem you have is you need to read the instructions for the webmail program you are using.