A few cameras allow copyright ownership information to be included in EXIF data that is automatically attached to files at the time of shooting, but this is not a common feature and is not where most people would expect to find it. If it is not a menu option in your camera, you can't do it.

The standard location is within IPTC metadata, specifically the copyright field. This will cause Photoshop to flag the image as copyright. It is also a good idea to include ownership information in the main "description" field used for captions, because this is the only field that many publishers ever look at.

Unfortunately IPTC is not written in camera, but has to be added during editing using software that understands IPTC. This could be Photoshop, for example, or a raw processor, or a digital asset management program - whichever suits your workflow. But beware that much lower-end photo software has no ability to read or write IPTC, and in fact erases all IPTC metadata  when saving the file.