It looks like the kind of thing my son has done with layering in PhotoShop.

From what he tells me, it sounds like a person with PhotoShop skills can do just about anything with a picture.

I Googled “combining images” and got some hits.
In those results I also see people calling it merging or blending.

I don’t think there’s a specfic name for that. As @Jeruba said, you use photoshop and outline areas, and pop in images of waves or splashes. It’s pretty simple if you know the software. My son showed me how to do it. He’s 12.

There are a lot of tutorials online that show you how to do similar things. Just look around for where they substitute one image for part of another.

I’d call it a kind of collage.
The way you do it is using masks and layers, as some have mentioned above.
Scott Kelby tutorials cover the techniques well. I’ve seen them one a few sites including YouTube, hunt around for him on the web.

There are as many different ways to accomplish the illusion as there are people using Photoshop. As was suggested, go to youtube, there are dozens of tutorials showing amazing effects and how to achieve them.

It looks like layers, which you can do in PS or Gimp. You would basically collect your images, greyscale them, then either use select and eraser or match background depending on your editing program. You could then move the layer to fit onto the person, once you have designed a positive space which to attach to the photograph image. I don’t know if it is a style as such, but more of an art work done by someone who knows the program quite well.

I would use the term blending modes and layer effects to search for tutorials.

One of the blending modes that is really helpful is using the layer mode multiply. Multiply takes the image on the top layer and blends it with what is in the layer directly underneath it. Playing with the transparency of the top layer and using preview mode you can vary the amount of opacity until you’re happy with the effect. To make it even more interesting you can make copies of the layers and alter the colors and special effects. You can play with filters and just keep layering and layering to your hearts content. You can turn the visible layers on and off to see how different combinations look. If you want to look at different options side by side duplicate the entire image and compare the different effects by turning layers on and off, shifting colors, applying layer modes like drop shadow, using artisitic filters etc, etc.ad infinitum.

Here is one simple link that explains a little bit and has further links to other blending modes further down on the page.

Here is a brief tutorial that runs through some of the common layer effects.

This technique is called Double Exposures. Usually you have to do it within Photoshop, there are many many tutorials on youtube for doing double exposures. However sometimes you can do it in-camera: http://www.youtube.com/watch?v=d2lHQJFJ-nc
But yeah the official name for this is double exposure.