So you can see the name change is an issue with the long standing inhabitants of one of the Bryn Glas Bach properties!
As was the baptism record of Ellen - I've deduced (wrongly?) that the "Eli" on the transcription records is a mistake despite the sex and name being changed. The dates, location and a search for an Eli on the GRO index suggest so.
As for my Jane and Robert Williams (my great * 2 grandparents btw) records of their time are fairly sparse for their time in Wales. I have another birth certificate of one of their children for 1882 Pen y ffridd Llanbeblig (Robert Williams) before a regular appearing in the census from 1891 in Liverpool (Hankin Street). Robert senior giving his mining experience to work on the ships. I have no other records of their time in Wales from birth to their move to the big city.
In summary this is what I have on the family (Robert Williams senior is the brick wall currently, hopefully!):
1891, 1901, 1911 censuses:
Robert (c. 1853, Caernarvon), Jane (c. 1856, Pwllheli), the children that survived were Ellen (1877), Robert (1882), and Margaret (1891) another 8 children didn't make it to 1911.
Jane's family (Roberts) I've researched extensively. I'm lucky to have a will that documents her and her siblings. Both David and Thomas Roberts were farmers, and I've made contact (and have a photo!!!!) of Ellen Roberts who became Ellen Pugh.
I also have know I have the right Robert (1882) and Ellen (1877) Williams (and hence locations) given their birth dates, 1939 censuses and their addresses in Liverpool that are known to my family.
Robert and Jane married in 1874 (per the 1911 census), though through extensive FindMyPast, Ancestry and GRO certificate purchases I've yet to find them tying the knot.
The other twist in this tale is both Robert (1882) and Ellen (1877) have a Jane Jones as their mother's maiden name. Could Jane have been married before, could their be two Janes? Queue another extensive research into Robert Williams and Jane Jones marrying in the 1870s!!
With no other (Welsh) records for Robert and Jane. (I still haven't got her birth certificate, though have her burial deeds, death cert in Liverpool etc) I'm focusing on the leads I do have their two locations at the time of their children's birth:
Bryn Glas Bach (looks like two properties) and Pen Y FFridd, Llanbeblig (looks like an area so makes connection more difficult).
As for the 1881 census - I have one potential 'sighting' of Jane with Ellen (but no Robert) in Caernarvon city but given they were a mining family (and no Robert) I cant be 100% sure.
So you can see why my spare room resembles some sort of police HQ investigation room with post it notes of prime suspects and a timeline trying to work through what evidence I have.