That’s what I did.
Here is my file in case anyone wants it.
Comment=TeamSpeak is software for quality voice communication via the Internet
The above goes into
$HOME/.local/share/applications/teamspeak.desktop, although that depends on your distro/preference. Another place where you can place the file is
/usr/local/share/applications/ for system-wide applications.
In my case I chose to use the more classic logo (teamspeak_logo.svg) but there are several you can choose from in
html/client_ui/images/icons/. Another good choice is tray_not_connected.ico if you like the zoomed-in headphone variant, but it may not work as well since it’s a .ico, although you should be able to convert it to a .png by using
convert tray_not_connected.ico tray_not_connected.png (included with imagemagick package).