legally speaking you have that copyright whether you mark them or not.
The visible watermarks you see on many internet-photos are there to make it less convenient for pirates to steal and use the image, in spite of the legalities.
No, you do not have to register yourself or the watermark anywhere for the copyright to "kick in" so to speak.
In reality it is nearly impossible to stop photo-theft if you post your images on the internet. As soon as anyone can see your picture on your computer, it means that you already HAVE a copy of your image on their hard-disk.
The best way to guard yourself is by:
- post only low-resolution images on the internet (640X480 or 800X600)
- have a visible mark/watermark on your photo
The reality is that the internet is a global domain. If you are a US citizen and some pirate in say Hong Kong copies your image and use it for a local website, the effort and money it takes to even get to the point of any legal action is enough to make you old before your time.
Unless you are an accomplished revenue-generating photographer, it's hard to prove any financial damage anyway.
The internet is not policed for such matters. The agencies trawling the net are after bigger fish and with the many trillions of images on the internet, you can imagine how impractical it would be.