Coffin Stainer or Stainer Coffin?

Jane Hemblen, half-sister of my great great grandmother, Elizabeth Hemblen, married William Stainer Coffin, on 7 June 1867 at Bath, Somerset.  William's father is named as Thomas Coffin, a baker.  Their relationship produced 7 children, whose births were registered in Bath registration district as follows -
1862 William Stainer Coffin Hemblen
1864 Thomas Stainer Coffin Hemblen (died 1865)
1866 Thomas Stainer
1869 Elizabeth Stainer Coffin (died 1870)
1871 Elizabeth Coffin
1873 Emily Coffin
1875 Samuel Stainer Coffin
1877 Charles Stainer Coffin

I have not found William Stainer / William Coffin in the 1841 or 1851 census of England and Wales, but in the 1861 census he is listed as William Stainer, a knife grinder, born at Wimborne, Dorset; and Jane Hemblen is listed as his servant.  In the 1871 and later censuses he is listed as William C. Stainer or William Coffin Stainer.  His death is registered under the surname Stainer and also under the hyphenated surname Coffin-Stainer.  When his wife Jane, died in 1892, her death registration identified her as Jane Coffin Stainer.

When their children married and had children of their own, the events were registered under the surname Stainer, but Coffin was often used as a second given name, resulting in many "Coffin Stainer" registrations.

In researching the extended family, I found several related family trees on the Ancestry.com websites.  Many of these trees did not identify the parents of William Stainer Coffin, while others suggested that he was descended from a line of Stainers, not Coffins.

I believe it more likely that William Stainer Coffin was a son of Thomas Coffin and Ann Beale Stainer, who married in Wimborne, Dorset in 1819.  Thomas Coffin is listed in the 1841 census of Wimborne, as a 40 year old baker with 4 children, and appears to be a widower, as no wife is listed.  Thomas Coffin's listed occupation of baker, matches the information from William's marriage certificate.  Two of Thomas Coffin's children listed in the 1841 census are Samuel and Emily, names also given to two of the children of William and Jane Coffin / Stainer.

Why William Stainer Coffin changed his surname we will likely never know, but my guess is that it relates to William's life prior to meeting Jane Hemblen.  In the 1861 census Jane is listed as his servant, but there is also a 6 month old daughter, Mary Stainer, living with them.  It is unclear from the census entry whether Mary is Jane's daughter, or William's daughter from a previous relationship. William and Jane had 3 additional children together before they married in 1867, so perhaps William was still married, and not a widower as suggested by the 1861 census record?