Yes, I thought of naming patterns, which were often used up until the mid/late 1800s, although less often after that when (thank goodness) different forenames were introduced. It was one of the reasons that I queried father Matt for your William, and also mother Margaret, because I didn't see those names for any of Wm's children. However Frances could well be correct - I had hoped her sister "May" was right because she would be easy to follow up with that name, but the 1841 census scan clearly shows Margt Cain 25 along with Matt Cain 67 and Wm Cain 15 (no relationships given).

If living in Douglas means that they were born there, there were only a few families with a William/Wm the right age, and in 1851 they were either still with their families after your Wm had married, or were unmarr servants. However if your William was one of the many Williams living elsewhere in 1841 he will be like trying to find a needle in the haystack.

There is one record which might give some clues, if Matt & Margt Quark/Quirk were Wm's parents, and that is their (assumed) elder son Thos bapt 23 Dec.1809 Saint George, Douglas. Strangely he is also recorded on an extracted record (from the parish register) as bapt 23 Dec.1809 Saint Mathews, Douglas. [Both from IGI] You could also trace Thomas through censuses and see whether these show anything about other family members.
There was also Ann bapt 20 Feb.1815 Saint Mathews, Douglas, and of course Margaret in 1811 (last message).
Matthias Cain & Margt Quark married 6 Feb.1809 Onchan [IGI]

Frances mentioned a bapt for the 67-yr-old Matt from the 1841 census which is probably Matths CAIN Christening: 26 JUN 1774 Braddan, Isle Of Man, Father: PHIL CAIN, Mother: CATH FAYLE [IGI].

You have probably seen Brian Lawson's burials index which has Wm Cain buried Braddan aged 54 on 2 Jan 1879, and Selina buried Braddan 14 Nov.1901?
Donna, is there anything else available in the burials/MIs about this couple please, or anyone else in their plot?

Sue