You can never be too fussy.
I am yet to determine what happened to Francis and Nicholas and I have also not yet really tried to identify William.
Well, that is not quite correct - several months ago I had a look and found that I did not have enough information to work with to decide between a number of possibilities for William.
However, there are no 'set rules' to say that certain names (or the names of certain relatives) have to be used when naming children.
We know naming patterns exist but they were certainly not always followed in any religious manner.
With your family we do have a couple of clues however.
William and Miriam used the name Charity twice including for their eldest child and first daughter.
And then William used the name once more with his second wife which is a clear indication the name was very important to him.
The logical reason is that Charity was the name of his mother.
If you look at the children of William from his first marriage it is interesting.
Charity (1767-1770) - William's mother
William (1770 - ) - William's father and also his own name
Charity (1773-1773) - William's mother
Thomas (1776-1843) - Miriam's father
Mary (1780-1780) - Miriam's father
Miriam died in 1781 and William then married Ann Vine and had the following children:-
Miriam (1783-1851) - first wife
Mary (1785-1793) - name of first mother-in-law but possibly also of Ann's mother
Grace (1787- ) - not currently known
John (1789- ) - William had a brother named John but could also be Ann's father
Susanna (1791- ) - not currently known
Charity (1793-1794) - once again for William's mother
There is definitely, for the most part, a pattern here.
But I did forget to mention that William had two further siblings:-
Alice Pearce bp. 30th April 1749 at Constantine
John Pearce bp. 20th April 1753 at Constantine
And there is yet another clue that this is the right family for your William.
Charity Pearce of Phillack was buried 9th May 1794 at St Erth
There is indication in the PR that she was wife of William.
There is also a burial for a William Pearce.
William Pearce of Phillack buried 9th January 1796 at St Erth
Now this 'might' be the elder William.
But I currently have this burial assigned to the husband of Miriam and Ann - i.e. son of the above.
But looking at it again I do think it more likely to be the elder man.
I think your William (husband of Miriam) is this one:-
William Pearce of Penpoll age 77 buried 12th January 1847 at Phillack
Checking IGI and there are other William Pearce's born around the 1769-1771 period but they are all from other areas.
The only one at Phillack or close by is the son of William and Charity.
I will try and look around a little later to see what more I might find on the other children of William and Charity.
CT