A company is a separate legal person to those behind it.
Xenia,
Here is a bit about stamp duty in SA
http://www.revenuesa.sa.gov.au/taxes-and-duties/stamp-duties/transfer-of-a-business
I think you are equating 'business' name with 'business'. ASIC don't regulate or provide information on transferring a business, just transferring a registered name.
Transfer of title.
What are you actually wanting to transfer? Business name perhaps, good will, assets.
Consider
1. stamp duty
2. CGT
3. Structure of company for
a) asset protection
b) tax flexibility
c) succession
d) minimising guarantees
4...