Yes, please go back and edit the names out

fascinating story.
Sands 1892 Suburban
PARRAMATTA, Phillip St, South Side, Charles St intersection
SMITH, William Engineer
NSW BDM online index deaths
1907 SMITH, Eliza (parents given names recorded as Thomas & Mary) registered Parramatta # 2408
From that dc, where was she buried? (I suspect it would be Mays Hill Cemetery, see below)
TROVE
http://trove.nla.gov.au/ndp/del/article/86155778 Cumberland Argus 16 Jan 1907
“Jan 9th, 1907, at her residence, Arthur Street Granville, (late of Phillip Street Parramatta) , Eliza, beloved wife of William Smith ….”
http://trove.nla.gov.au/ndp/del/article/86162083 Cumberland Argus 12 Jan 1907
“Mrs Eliza Smith, of Arthur St, Clyde …… funeral took place on Friday, moving to the Presbyterian cemetery, Western Road (I suspect this would be Mays Hill Cemetery). “
Sands 1909 Suburban
GRANVILLE
(including Clyde & Guildford) Arthur St (Duck Creek to Prospect St) East Side : (consecutive numbering)
at no. 5, SMITH Charles
at no. 8, SMITH William P (notice the “P” I speculate that would be P for Peter.
May I note that although Onslow St (Sydney Rd to A’Beckett St) is listed in that directory NO householder in Onslow St is listed with surname SMITH
Sands 1910 Alpha
Charles W SMITH, Harris St PARRAMATTA
William P SMITH, 8 Arthur St GRANVILLE
NSW ER 1913 HARTLEY, polling at Katoomba
Donald AIKEN, Park St, plasterer
Edward Imlay AIKEN, Wilson St, engineer
Muriel Annie AIKEN, Wilson St, domestic duties
(I note that you have the AIKEN family in 1907 at Osborne Villa Lett St, however, Wilson and Lett Streets intersect)
There are many instances in the pre WWI decades where Mum has a large family, spread over perhaps 20 – 25 years, and where the eldest girls may be having their first babies while Mum is still adding to her own family. Sometimes the girls are single lasses. Sometimes (often) Mum raises the girls babies along with her own, and the girls are then able to find work locally, perhaps as live in domestics during the week, and return home occasionally for a half day visit. But usually the baby is registered showing her natural Mother as the Mum and Gran perhaps as one who assisted the midwife.
When I was sorting out my various NSW SMITH lines, I found it very important to obtain the NSW BDM records before trying to sort out the various bits of oral history about my SMITHs. That way I could then place the oral history to the correct immediate families. I think it is also important to make sure that you are ordering full NSW transcripts rather than partial ones, as quite often the very clue to unravel the SMITHs is found in the obscure information (eg relationship of informant to the subject). Of course, you will remember that the information on a birth certificate is NOT provided by the infant, and information on a death certificate is not provided by the deceased, so the information provided on a marriage certificate comes from the two subjects themselves.
There is still nothing illegal in using a name that is not the name on your birth certificate. Of course, in NSW you can still be known by various names without formally changing your name ….. of course, providing you are not doing so in a criminal sense to avoid punishment. It is simply a little more difficult today to do so, as you usually need to provide identification documents to open a bank account or enter into a commercial contact etc.
Cheers, JM