I never use Watermark and have no knowledge on how to move it (tried but couldn't), but there are other ways to make a watermark if the Image>Watermark doesn't work for you

New Image, big enough to take your name, transparent background.
Text tool, write your name or whatever you want to use as a watermark.
Merge Visible.
Save as a .PSPImage file.
Open your photo, add the newly made name, hit K for the Pick Tool, move the name to where you want it.
Set the Layer Blend mode to Soft Light.
Or experiment with other Layer Blend Modes.
This way you have control instead of the program.
In case you are wondering why my Layers Palette looks different from yours (if it does).. I have enabled the Right Pane in General Preferences>Preferences>Palettes
Joëlle