Legal Question in Business Law in California

You may photograph a 17th-century artwork, and you may then copy or display the image (among other things). You can also acquire permission to use someone else's copyrighted image of the artwork and only then may you use it. Whether you may register and use an image of the 17th-century artwork as your trademark or service mark depends on whether someone else has claimed it already. Try a search of the USPTO and/or Google Similar Images.