Hello :-)
I wouldn't be too sure that "Parry" was anything more than a middle name - whilst it was common is the US to style a woman's name as first name/ maiden name /married surname, it wasn't so much (if at all?) in the UK at that time (someone will correct me if I'm wrong! :-)
I would be more inclined to consider "Parry" as her mother's maiden name, or a Grandmother's name, or a family name. There were a few "Jane Parry Davies" in the records, especially Wales over the years.
Just a bit more for the records (you may well have this):
I would be fairly inclined to believe this to be Jane in 1841. The age is not quite right - this census supposed to round down to nearest 5 years, so your Jane should be 20 or 25, but mistakes in applying the rule were common and so were mistakes if the person didn't actually supply the information (ie: in a Lodger/boarder situation), Born in Surrey (Y) fits, and "Ind" Independant fits
The way the Census is laid out, infers none of the household are connected to each other or in any family group
1841 St George The Martyr, Southwark, Surrey
Elizabeth BOWLEY 55, Druggist, N
/
Jane Parry DAVIS 30, Ind, Y
/
John A SAYER 35, Druggist sh, N
/
Henry RICKARDS 15, Druggist Ap, N
/
Mary BROWN 25, F.S.
//
The 1863 Burial you found is definitely her - Edward died 1874 and is buried with her:
BURIAL RECORDS - West London & Westminster Cemetery, Earls Court, Old Brompton
Jane Parry Davies #34702
4 Allens Terrace, Kensington
Buried 17 Aug 1863, aged 46
Private Grave, Ref: A, 77.3, 4.3
Remarks Extra Depth to 10ft see 75700
Edward Davies M.D. #75700
1 Uxbridge Villas, Paget Road, Shooters Hill
Buried 10 June 1874, aged 69 years
Private Grave, 2nd Internment, Ref: A77, 3x4.3
Remarks 34702 B.R. Opened to 8ft
Edward left a Will, probate 17 June 1874. Effects under £1500
Inspector General of Hospitals and Fleets, died 4 Jun 1874
Proved by: John Henry Plowes of 39 York Terrace, Regents Park, Middleses, Esq, Sole Executor
Cheers
AMBLY