I have googled many keywords such as "ghost frames, databending, echo effect, hall of mirrows, etc." but to no avail. I have also tried the time echo effect in After Effects but it doesn't seem to work.
One way would be to use the liquify filter. You can tell it to not stretch certain areas, then take the pinch tool, and drag it out into streaks. Its keyframeable, so that's an option. You can also do a mask with horizontal blur. Basically, create 2 of the same layer, bottom layer be the blurred version, and top clean plate, then mask around what you want to keep straight and then feather it out. You can also do the same type of technique by adding it to an adjustment layer and masking what you want clean/blurry and then choosing add or subtract respectively, which is probably the better way to go anyways. Hope that helps. There are probably other ways to do it, but that's the 2 ways I can think of off the top of my head. I'd have to play around with it more to see if I can find others.