What I need it to do is take a screenshot of an area of my screen when I press a hotkey, and save it automatically to my computer. Now, the difficult part, and the part I've been having a hard time figuring out, is I need it to be able to save all of the images using the SAME name for every image, but a different directory. For example, if I'm watching a video, and I want to take a screenshot every time I see a hot dog, I can set it to save every image as "hotdog.jpg" and it will for example make a directory with the date and time (accurate to at least the seconds place, to allow me to screencap in somewhat rapid succession) and save the image called "hotdog.jpg" in that folder. I don't really care about the naming scheme of the directories, as long as it is such that they will appear sequentially. The images MUST be able to all be saved using the same file name, though.

There is a very good reason why I must be able to do this, so telling me to just use different names and rename them afterwards doesn't work. If I wanted to do that, I'd just use one of the multiple free programs I've already tried. Also, something free is preferred over something that has to be paid for. Open source is preferred most of all, if available.
Well the problem with the snipping tool is that I have to select the area manually each time, and save each file manually. I meant something more like ZScreen, where you can select the area you want to capture beforehand, and then just hit a hotkey each time you want a screenshot and it will save them automatically. My problem with that program is that I don't believe it's possible to do what I mentioned before, of saving each image with the same name to a different directory.