If you cannot see your MIDI controller type listed in the Ableton > Preferences > Link MIDI > Control Surface dropdown menu, it's likely because you're using an old version of Live.
Ableton adds control surfaces to the Ableton Control surface list as and when they're released. If you have a version of Ableton Live installed from before the controller was released, it will not support your new MIDI controller.
If you update to the latest version of Ableton Live, you'll see your controller listed as a control surface in Ableton Live.
You can download the latest version of Ableton Live from your account page on the Ableton website.