Having explored this all further, thanks to your help, I found that Charles had a younger brother called Samuel born 1841.
He married and then named a son, Samuel Cooper Hibbard, in 1868.
He also has the habit of randomly using middle names and then not. On different census records, one or two of his kids get middle names, and then not on others, seemingly at random.
So clearly Cooper meant something to the family. I may never know.