I cannot think of an "industry term" for what you want, but in general, it's hiding identity, or obscuring license plates, etc.
As Harm mentions, the use of Mosaic and/or Blur, limited to just the area that you wish to affect by Track Matte Keying, will get you exactly what you want. Once you decide on how much to obscure the faces, you will then Keyframe the Fixed Effect>Motion>Position (and maybe some Motion>Scale) on the Track Matte.
In general, one would place their footage onto Video Track 1, Duplicate that onto VT 2, where the Blur, Mosaic, or similar, or a combo of them, Effect(s) would be added. Then, one would create a Track Matte (could be an elipse in Titler, or more intricate Matte in PS), locating that onto VT 3, and then apply Track Matte Keying to that Duplicate Clip in VT2, linking it to the Track Matte in VT3. As the subject moves, one would animate the Track Matte to follow.
Good luck,
Hunt
