What is the terminology for AR text in a video?
There's not much to it, the effect could be called "3D tracking Text" or something like that.

Open up After Effects. Load up your file that you want to put the text in. Use the camera tracker that natively comes in After Effects. Now, you can attach a null to one or more points that are automatically generated and detected, which will follow the geometry and movements from the footage. Once you're happy with where the null is positioned, you can create a new text layer and parent it to the null, so that the text is following its position, rotation and scale. That's it.

Creating a 3D-Text however is a different story. For that, you could use the element3d plugin for aftereffects, but that's quite expensive. Alternatively, you could track the camera and export the tracking data to a 3D-environment. I'd recommend using pfTrack for the tracking part. Then, inside the 3D-Program (like Cinema4D, Modo, 3Dsmax, Maya, etc.) you can import the tracking data which will give you a camera that matched the movements of your footage. If you then just place an object, like 3D-Text in the 3D-Space and render the footage from the perspective of the aforementioned camera, you can place that footage on top of your original footage and the object will stick.