A lot of different people were connected with Hammond Turner & Sons (etc) over the years. Here are just some of them. I will add a link to a simple family tree when I find a suitable way to display that information. There is more information about some of these people on the first page of the Wills section.
John Turner 1764 - 1839
As well as being the father of the brothers mentioned below, John had two other sons. His oldest child (born around 1788) was John, about whom little is known (he died, aged 33, in 1821), and the youngest was Alexander (born 1814). He also had two daughters, Jane and Marianne. Thanks to careful research by Keith Winters (see Links for more details), I now know that John was married twice: the mother of his seven older children was Sarah Ketley, who died in 1804. Alexander's mother was Susanna, who married John in 1811. John was the son of John Turner and Mary Hammond: she was the sister of Samuel Hammond. John ran the button-making business with his uncle Samuel Hammond, hence the middle name of two of John's sons.
The date from which John chose to add Hammond to his sons' names gives a possible clue to the date at which he joined Samuel Hammond's button making business: John (born 1788) and James (1792) were not given the name, but William (1800) and Samuel (1801) were. Interestingly Henry (1803) wasn't given the name: perhaps enough 'favour' had been 'curried' by then!
William Hammond Turner c. 1800 - 1851
Partner in Hammond Turner and Sons with his father and brother(s), married Elizabeth Nunns and had two daughters. He was living in London when he died, and had a connection with Charles Weldon, button maker of London.
Samuel Hammond Turner 1801 - 1841
Son of John Turner, married Elizabeth Woodall Bragg with whom he had nine children: they became orphans when their mother died two years after their father.
Henry Turner c. 1803 - 1866
Brother of Samuel and William Hammond Turner and sometimes referred to in legal documents as a partner in the business Hammond Turner and Sons.
James Turner 1792 - 1867
Another brother and partner in business Hammond Turner and Sons. He married Anna Maria Pemberton and they had six daughters and one son, John Pemberton Turner, who wrote an article which is quoted in full under 'History'. James went in to business with his son, possibly after the premature deaths of two of his younger brothers William and Samuel.
John Pemberton Turner 1824 - 1886
Ran a button-making business in Manchester and Mytholmroyd, Yorkshire, with Thomas Bate and one 'James Turner', who was probably John Pemberton Turner's father. The company diversified after the civil war, during which - under the name Hammond Turner(s) and Bate(s) - they made some very fine buttons for the Confederacy.
Those brackets are intended to show the confusion surrounding the company's name: there were two Turners, one Bate and no Hammonds in the partnership but the name is often written Hammond Turner and Bates, including by me! Evidence I have just uncovered suggests that it is most likely to have been Hammond Turners and Bate: the overpinting on the stamp on the page linked under JPT's name shows it that way, as does evidence they submitted to a parliamentary enquiry (also mentioned on that page).
Even more excitingly I have photographic proof that that is how the name appeared as a button back mark: a button in the National Railway Museum's collection in York, made for the Lancashire and Yorkshire Railway Company, shows the back mark Hammond Turners & Bate Manchester. The front and back of that button, using photos taken by the NRM, appear in the back marks gallery.
Samuel Hammond 1740 - 1825
Button maker: business partner and uncle of the John Turner mentioned above. An earlier John Turner, father of the John Turner listed above, married Samuel's sister Mary. Samuel's brother Thomas was the father of Bonham Hammond, listed below.
Bonham Hammond 1769 - 1807
Button maker, another of Samuel Hammond's nephews. His name appears in directories after that time with the words 'executors of' - his will (available on the Wills page) left specific instructions about how his business affairs were to be handled after his death.