If you are still looking for the answer to this puzzle:
Daniel, Adam, John and others were all children of Joseph and Ann Bl(e/i)nman Norman, a shearman of Shepton Mallet. In 1841 Adam and Daniel used the surname Blenman whereas John and father Joseph were both Norman; but they all used Norman after that.
Joseph Blenman Norman died in 1850 aged 80, so is likely to be the Joseph Blenman born illegitimately in 1771 to Fanny Blenman in Croscombe (next to Shepton Mallet). My guess, therefore, is that either Fanny married a Mr Norman some time after 1771, or she died and Joseph was looked after by the Norman family, so he (and his children) used both surnames.
Unfortunately I haven't found any evidence for either of these theories, although I did wonder whether Joseph named his first child Daniel after his stepfather.
Richard