A common problem, census enumerators and vicars clerks wrote down names as they heard them, more often with church records, the vicar wrote the names on a piece of paper, screwed it up, put it in his pocket and passed it to his clerk weeks later. I could show myriad examples which do not have a Birmingham connection, but one that does is my great grandfather, Durows, probably originally DuRose, but variously over censuses, Darrow and Durries. It makes the search far more interesting and in the case of my family means that at least one DuRose family is actually Durows by birth.
Bob