What is the profession of adding special effects to a video called? Using programs like Adobe After Effects, for example.
I am looking for a name other than video editor since in my interpretation that describes a job of arranging the video in a sequence, using video editors like Adobe Premiere Pro or Sony Vegas.
I’d say “Post-production visual effects” for the general process. Visual effects is often shortened to VFX. “Post-production” separates it from work done during filming, such as involving makeup, props, practical effects etc.
The job roles vary from “Visual effects supervisor” or “Visual effects director” on large movies, down to the individuals who are usually (I think) called Visual Effects Artists. I think this (Visual Effects Artist) is probably what you’re after.
For more detail on job roles, see http://creativeskillset.org/creative_industries/vfx/job_roles