Hi,
It was not, and still is not, compulsory for a person to complete a deed poll to change their name in NSW.
Any person can choose to be known by another name without any formal process required by NSW statute law, provided of course that they are not doing so with intent to deceive or defraud.
Sometimes it seems a person has changed their name, particularly when researching in NSW in the 1860s - 1900s and then with deeper searchings it is variations in spelling or mis-transcribed index entries or similar.
Sometimes a complete surname change occurs when the person is a child and his/her mother's known by surname changes through a marriage (even a commonlaw marriage). From 1856 until around 1969, the registration of babies born in NSW did NOT include a surname for the baby. So the baby became known by his/her mum's THEN surname. If mum were married, she would usually be using her husband's surname, so all her children at that time were usually known by that surname. If that relationship was ended (death of partner or otherwise), and mum formed a new relationship (formal marriage or otherwise), then she may have become known by that chap's surname, and so too her children.

**
If you care to share the name from the 1860s, and some background, I am happy to see if any of my offline resources can find him/her in NSW in that decade.
**
No paperwork system needed

By the 1970s, changing name by deed poll was becoming the accepted process but it is still not compulsory.
JM