Driver’s licences & vehicle registrations are issued by each state.  It is best to change your driver’s licence first is will make other changes easier down the track.  Changing the name on your driver’s licence is a free service, but your old licence must be surrendered.  This process needs to be done in person and you will need your existing licence, potentially other identity documents to achieve 100 point ID check and either your original marriage certificate or a certified copy.  An appointment is usually not required.

NSW    Roads & Traffic Authority  
    Roads & Traffic Authority name change information   
    Phone  13 22 13

VIC    Vic Roads  
    Vic licence name change information   
    Phone    13 11 71

QLD    Department of Transport
    QLD licence name change information  
    Phone     13 23 80

SA    Department of Transport  
    SA licence name change information  
    Phone 13 10 84

WA    WA Licencing Services  
    WA licence name change information  
    Phone 13 11 56

TAS    Department of Transport  
    Phone  1300 135 513

ACT    ACT Road Transport Information  
    Phone  13 22 81