Re Name changing: *Joseph Stephen Allingham was known as Stephen in SA. [I have 14 generations of chaps named John Corsane in my F/Tree and I sorted them out- so there is hope.]
Just to clear up about Jane Allingham (my direct ancestor, the mother of the William Jones who married Maggie Bowden-Tatchell)? I think she is the Jane A. born 26 March 1848 and is there a citation for the birth record? It fits what I have. I have her siblings James (b Abt. 1846) and *Joseph Stephen Allingham (b. Abt. 1845).
I have her as Jane Allinghame b. 1845 in Dorset, dau. of James Allingham and Ann Short; m. 31 Dec 1869 in Registry Office Strathalbyn, Sth Australia. And no death record for this Jane Jones who presumably died in SA.
Jemima appears on the 1861 England Census, Ref. RG 9/274 p. 17, lists lists William Allingham (b. abt. 1785, at Aldgate Middlesex) living at 1 Queen St, St Botolph Without Aldgate, with his unmarried daughter, Jemima Cole aged 46yr also b. Aldgate, Middlesex.
That means she was born after Jane Allingham and as Elizabeth was still alive, this may be another family. Our William came to SA soon after the death of Elizabeth, arr. aft. 1861, date unknown, and settled near Nairne, SA.
Now I need to work out from all this, who are the parents of William Allingham (Abt. 1785; d. 12 Sep 1873 at Mt Barker Springs- husband of the Elizabeth who d. 12 May 1860, Canford Magna, England). And then tackle Elizabeth's Identity.
It is nice to have this help from you but I wish I had access to the sources that you use.I have only got the BISA and Indexes of births in SAfrom 1842-1906.