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In order to add your copyright information when importing images into Lightroom you can create a Metadata Template.
This Metadata Template can also be used to add your copyright information to images already in your catalog. Social media sites such as Flickr, Google+ and 500px preserve this information. Sites such as Facebook, however, strip the information from your images. If you are concerned about this I advise posting to a site that preserves the information and then posting a link to this image on Facebook.