Hello Lily
This is a Welsh puzzle!
What you've possibly found is not the full patronymic (ap/ab etc) , which had practically disappeared from Wales by this time, but the intermediate stage. This was still used in some areas into the 19th century, especially in this area. It is very confusing as a person might be known by both x (father's first name) and x (father's second patronymic name) in different contexts and by different people. For example in parish records, one minister might use the semi-patronymic form and another might use the surname form for the children of the same parents.
I notice that in the 1841, Richard was entered as 18 but then the enumerator has corrected it to 15 (rounding down ). This would fit with your Richard's birth date. Also, I note that William Richard's occupation was entered as 'J' - as were a number of others in the book. The enumerator appears to have use three different types of J: a round looped J that he used for all the occupations and some first names; a pointed top loop J for other first names; and a J above the line for surnames such as Jones. I think the J in occupations might refer to 'journeyman' - I'm not too sure of the quarrying occupations but some were fairly skilled. There is a site for the North Wales slate quarries but at the moment, I can't fined it. I'll do some further searches.
I can't find a Richard Richard(s) who matches in the 1851. By 1851, William Richard is widowed and his daughter, Mary Richard, is the only one of the children left. He is down as a Quarryman, b. Mallwyd, Merionethshire.
From the evidence, I would say that you could be 85-90% confident that you have the correct family. It might be worth checking up on brother Howel/Hywel and his mother Mary's death certificate (1841-1851)
Good Luck
Gadget
