A quick scan of answers seems to be examples of birth names never being used, not why someone changes after many years.
I know of a change by a teenager.
I cannot remember why, but some time in early teens she stopped being called by birth name and used, possibly, her second name. This was announced by her parents, so that, for example, if we sent Christmas cards and named all the children on the card, we should use this new name.
By her mid-twenties she was back to her original name, cannot remember that being announced, she was just referred to by her parents under her old name.
A colleague at work changed his first name because too many people thought he was a she because in many countries his name was only used by females. If one is dealing with clients in Asian countries it does make a difference. So in all official work-related documents his name changed, however he kept his original name for his private life. This would mean that, with a surname such as Smith or Jones, it would look like 2 separate people had worked for the company.
Neither of those examples explain William/Thomas. Sorry.