Even though there is no option to edit the chat window header by default, you are able to edit it using Custom CSS. To do so, navigate to Configuration > Chat > Chat buttons > Edit your chat button. Then in the "Chat window" tab scroll down to the "Custom CSS" section and add the following CSS code:
.InfoPanel {
background-color: black !important;
border-top-left-radius: 8px;
border-top-right-radius: 8px;
}
Do not forget to APPLY the CSS code and SAVE the chat window.