What is the name of this port/jack on a cell phone?

It's a connector for an external antenna. Typically this is used in cars for handsfree operation for phones made before the age of Bluetooth. The dashboard phone cradle/holder which hooks up the phone to the car's audio system and microphone can also have a matching connector for a roof-mounted antenna which gives you better reception.

That looks more like a camera than a port...but I assume you know your phone better than I do. x) What kind of phone is it? Look up the specific type of phone and you can most likely find a manual or a guide that shows you what's on your phone's exterior.