Within Teamwork Chat you can quickly edit your chat handle that other users will use to create to chat to you.
Click on your profile dropdown menu and select Profile.
In your profile settings, you will see a Handle field. Here you can update the handle text.
By default, the handle that will be chosen for you is your first name however if another user already has a handle with your first name, then yours will default to your first name and first letter of your surname.
For more information on using handles see: Settings within Teamwork Chat