Name
Gradient color wash/gradient color overlay/gradient tint

Bonus
The video appears to be a combination of applying a tint to the video, a little blurring and some time remapping, possibly using a plugin like Twixtor. Filming at 60fps or higher would help facilitate the slow motion/time remapping. Similar speed effects could be accomplished natively in a lot of video editing software without paying for Twixtor.

How-To
AdobeTV has an instructional video titled Using a gradient fill to add a color wash that will teach you how to pull off the effect.

Photoshop's "Duotone" color mode can produce results like a lot of these simpler examples, but you could also get results that look the same by converting to grayscale and then using the "Hue/Saturation" image adjustment.

An image search for "duotone photo" might get you some of the results you're looking for.

The more complicated examples, like the first one, Red Collar, seem to be a combination of gradient and painted-on color washes.

This page has a few Photoshop actions that accomplish similar effects. Check out the FREEBIE V and Rainbow Haze ones in particular.

To accomplish an effect like you see in the Red Collar example, here a slightly different technique than the one in the AdobeTV video:

1. Image>Mode>Grayscale (must convert to grayscale before duotone)
2. Image>Adjustments>Hue/Saturation
3. Check the "Colorize" box
4. Adjust Saturation, Hue, Lightness for one of the colors you want to use
5. Duplicate the layer and repeat steps 2-4 for each additional color you want
6. Select the top layer
7. Layer>Layer Mask>Hide All (or reveal all)
8. Apply gradient or paint on areas in layer mask to show parts of the layer
9. Repeat on other layers as desired

Here's a quick example I created using this process:

Additionally, it seems like some of the color schemes in those examples are inspired by lens flares and washed out lomography photos. Here's a search for "lens flare lomography".