Hi Mike,
Referring to Elizabeth daughter of John Rowland as Elizabeth Jones (Jones derives from John) is the normal old Welsh system of patronymic naming. (There are lots of helpful messages and links on RootsChat about this). In the same way William, the groom, is entered on the marriage certificate as William Williams, named patronymically after his father William Jerman. The marriage in 1860 is rather late to be seeing examples of patronymic names but is not unheard of in rural Anglesey. Looking at the register for Aberffraw marriages in 1860, most are conventional names but there are other examples of patronymic names - John Jones, son of John Richards was married 17 Jan and Thomas Williams, son of William Jarman (and older brother of William Jarman) was married 4 May.
As for the 1841 census of John Rowland and family, the record was written by the enumerator and gives the head of the house in full - John Rowland - and gives the first names of his wife and children followed by 'ditto' referring to Rowland. The family was probably illiterate, certainly Elizabeth Jones and William Williams were illiterate when they married - they signed by mark - so it would have been the enumerator who decided how the names were recorded.
What I find most interesting is that William (and Thomas his brother) have the patronymic Williams, rather than the 'family' name Jarman when they married, although they continued to be known as Jarman (Jarmen, Jerman etc) in later life. This name is not common on Anglesey and does not seem to be derived from a forename like most common Anglesey surnames. I have uncommon surnames among my own Anglesey ancestors - Tyran/Teyran/Tyrer and Willins/Wellins - (the same problem with various spellings!) and I'm interested in where such names come from, so I've researched Jarman a bit more.
As mentioned - William JERMON son of William and Mary (maiden name) Jones - 6 Nov 1838, Aberffraw - seems to be William's birth registration.
The census records for William (senior) and family for 1841 - 1871 show them in Aberffraw. William (senior) was born Amlwch (according to 1851 & 1871, he was also recorded as blind).
There is a baptism at Amlwch 5 April 1794 of William, son of Lewis GERMAINE (another spelling!), tailor, and his wife Lucy. Lewis Jerman, tailor, lives in Aberffraw in 1841 & 1851. He is aged 82, born Carnarvonshire according to the 1851 census. I haven't looked for Lewis in Carnarvonshire records.
William Jerman married three times, all at Aberffraw:
William Jerman/Jane Owen - 31 May 1819
William Jerman (widower)/Elizabeth Jones (widow) - 5 Mar 1825
William Jerman (widower)/Mary Jones - 26 Jan 1830 (One of the witnesses was Lewis Jerman by mark)
The following deaths occurred at Aberffraw:
William JARMEN 13 Aug 1871, age 77 at Church St., woollen weaver. Informant Ann Lloyd.
Lewis JARMAN 10 Sep 1856, age 87 at Chapel St., tailor. Informant Jane Evans.
Anne JERMAN 15 Nov 1847, age 75, wife of tailor Lewis Jerman who was the informant.
Mary JERMAN 21 Dec 1875, age 74 at Chapel St., widow of weaver William Jerman. Informant Ann Lloyd, daughter.
Regards, Idris