you will need to complete this as the first step to getting married.
Likewise, if you have misplaced the death
certificate of your previous spouse you should apply
for a new one.
You should apply to Births Deaths and
Marriages in the state in which you were born or in
which the death was registered.
For change of name applications you should apply to the state of your birth OR if you were born overseas, to the state in which you are resident. If you wish to change your name before marriage (perhaps to reflect the name you are known by if that differs from the name on your birth certificate) you need to start that process immediately as it can take quite a while.