An issue with the english language is that prior to the 19th century there were no "standardised" spellings. Life was centred on the locality, be it village, town or hamlet, and the great majority lived their lives without ever venturing more than a dozen miles from where they were born. Names could not just be spelt differently but could be pronounced differently over a region, let alone the country, even where the spellings coincided.
Around here we have the Redheugh bridge and the Derwenthaugh bridge. Redheugh tends to be prounoced "red-hyuff" while Derwenthaugh tends to be pronounced "derwent-hoff". Both Heugh and Haugh seem to have the same source but spellings have differed over time, even though they are less than five miles apart. Another place, Catcleugh can be "cat-cluff", "cat-clyuff" and "cat-clew", depending on who you ask.
Technically, each pronounciation of Claughton is correct for the locality in which it is found because it is the custom and practise of the place in which it is used. An extreme example of choosing how to have a particular name pronounced is the old BBC TV sitcom from the early 1990s called "Keeping Up Appearances" in which the socially pretentious Hyacinth Bouquet always (and repeatedly) insists that her name is pronounced "Boo-kay" (like a bouquet of flowers) and not "bucket" like the local usage has adopted.