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Apparently Richard Burton didn't like signing his autograph as he didn't like it and there are many variations. i have attached a photo of one that I had checked out by the Richard Burton Museum and Autografica although a few people on here disputed its authenticity), so there is a lot of discussion on the subject. I have also attached one sold with JSA approval, as you can see the 'd' of Richard is quite unusual. As for your copy I wouldnt like to cast an opinion, but at least you can compare some examples
I think the Hamlet photo is authentic - there are some leftovers from his early 1949 signatures to be seen.