All users have one unique URL where everyone can chat with the user. So you can share the url to give them direct access to you. This link is for ComeCat official user support.
You can find the URL by clicking "Connector" in side menu.
And in "Web" tab which is opened by default, you can find your URL of web chat.
Customising WebChat appearance.
You can change appearence by editing your profile. Please click "Edit Profile" link in side manu.
Here you can see what parameter changes in web chat design.