Hello, are you a relative? He didn't legally change his name, so there is no official documentation. We have handwritten letters by him, to his family in UK. Within these letters he shows a conflicted personality. There were definitely emotional issues between himself, his parents and certain siblings. My personal thought is that he wanted to identify himself separately from his father George. He clearly adored his mother, writing to her only and repeating that he wanted to prove himself to his father.
With the help of dates, addresses, details on his marriage certificate & stories he told his children, all matching that of his UK life and his photos we concluded that he is the same person. It explained so many odd things about his life.
So in conclusion, there isn't any official evidence, but to his descendents, we are satisfied that George Augustus Hayles lived and died in Australia as Peter Augustus Clayton.