Yes, you are instantly the creative owner of the photographs. You have the right to put a Copyright mark on them, or watermarking.
I created myself a little "Stamp" in GIMP which works okay. I also created my logo/name as a seperate image, in a variety of colours with transparent backgrounds. I open the image as a new layer in my photo, place it, size it, and merge the layers together. Pretty quick and works well.
However, I'm a big fan of the more open-form usage rights system known as Creative Commons.
Instead of "Copyright", you can use a CC mark, and attribute the image as non-commercial non-derivative or whatever mixture of licensing suits you best. For example, you can decide that people are allowed to make derivative works using your images, but they can't make money off it. You can decide that the image may be freely shared, but never sold. You can decide whatever you like.
Then, if people want to use an image for anything, the can simply contact you and you issue the image to them under a specific instance of the Creative Commons.
You can read more about CC in SA here:
Creative Commons SA - Learn More
or check out the Wikipedia Article to learn more about CC internationally:
http://en.wikipedia.org/wiki/Creative_Commons