changing name and property

I own a home, which is currently under mortgage. I had to change my last name, as it had incorrect spelling.
how should i get this changed. i can do via a solicitor. anything or department i should contact directly and provide them required details about my Name Change Certificate from NSW??

Before name:
first name: john smith
last name: liddell hearne

full name: john smith liddell hearne

changed name to
last name: hearne
given name: john smith liddell

full name: john smith liddell hearne

thats kinda the situation.. which dept should i contact..