The 25-year-old retained his IBF Australasian and WBO Global light-middleweight titles when Horn threw in the towel at the end of the eighth round at North Queensland Stadium and was quick to stake a claim to his own identity.
"I just want to let everyone know my name's Tim, not the son," a delighted Tszyu said in the ring after his victory.
"This is only the beginning."
His father Kostya was undisputed light-welterweight world champion around the turn of the century after moving to Australia from Russia.
"People are always saying I'm always getting opportunities for one reason and that's my last name and that I haven’t proved myself," Tim told Channel Nine on Thursday morning.
"But I had to say that I am my own man and I have accomplished stuff my last name hasn't given me. It's Tim Tszyu at the end of the day."
A battered and bruised Horn, who famously stunned Manny Pacquiao to win the WBO welterweight world title in 2017, said after the fight that he would be considering his future in the sport.
He also predicted a bright future for Tszyu.
"He is now the number one in Australia .... he can fly that flag for Australia," the 32-year-old said.
"Tim has that hunger about him. I've been there and done that. Tim is very hungry for that win and I can feel that through him tonight.
"He's got that champion’s spirit in him, I can feel it."
(Reporting by Nick Mulvenney, editing by Peter Rutherford)