Once your wedding ceremony has concluded the celebrant or priest then has to lodge the documents to that state department of Births Deaths and Marriages to register the marriage. It is then that you are able to apply for a registered copy of your Marriage Certificate that has your marriage registration details on it. This is the certificate that you most commonly need to get to prove that you are now married.
Spouses do not have to change their names after they marry. And to change you surname to your spouses surname generally doesn’t require a formal change of name with the Births Deaths and Marriages. If you are thinking of changing your surname to a spouse surname then generally the Registered Copy of your Marriage Certificate will be sufficient to prove you are now married.
If you are in doubt contact your celebrant, priest or the Births Deaths and Marriages.
See my detailed explanation on my legalities section of my website for more detail.