No. The Marriage Certificate presented on your wedding day is merely proof that your marriage took place and is known as a Couples Certificate. The reverse side of the Marriage Certificate advises of this situation.
What you will need for a change of name purposes is the registered Marriage Certificate issued from the Registry of Births, Deaths and Marriages (BDM). BDM, however, charge a small fee which normally is over and above the fee you pay to your Marriage Celebrant. However, many Marriage Celebrants will be happy to facilitate your application to BDM if you wish, by submitting your application (and payment for same) at the same time as they lodge the other marriage documents.
Additionally, you should also be aware that you will need the BDM registered version of your Marriage Certificate to change your name on your passport and on your driver's license.
Also, Professional Registration Boards (e.g. Medical, Nursing) and some employers will only accept the BDM version for a change of name purposes. Please check with your employer as to their requirements.If you are not changing your name, you are not obligated to obtain the BDM registered Marriage Certificate, this then becomes a matter of choice for the bride/groom.