My 2nd great grandparents Edward Sleep and Charlotte Hancock had their first child William Joseph born on 29 Dec 1854 in South Australia.
The Place of Registration (Page: 207 Volume: 6) was given as The Murray, South Australia.
Being from South Australia originally, I am familiar with the River Murray (or Murray River) and places like Murray Bridge, but I have not been able to determine where "The Murray" would be. Presumably it was the name of a registration office (and not necessarily a locality in its own right) but was it in a town called The Murray or in another named locality?
As commented by @ColeValleyGirl The Murray was an electoral district. However, this was only from 1857 to 1862 i.e. a few years after this birth was registered. Consequently, I do not think this will be the answer, because I suspect that it would have encompassed a very large area.
Ancestry.com. Australia, Birth Index, 1788-1922 [database on-line]. Provo, UT, USA: Ancestry.com Operations, Inc., 2010.