Angelica Page was born a Torn but she has legally changed her name to honour her mum.
And she tells BlogTalkRadio.com, "As I get older I have more and more in common with my mother and less in common with the Torn side of the family.
"I'm the only daughter of my mother; I have twin brothers. My father has some other children from different marriages, so he's got a big gaggle and I just felt nobody was carrying my mother's name on and there were a lot of Torns.
"It just felt right and it felt like (it was) time (to give her) equal billing."
Page died in 1987, aged 62.
The theatre star has legally registered her surname as Page, after her mother Geraldine Page, insisting she wants to "honour" the screen legend and distance herself from her famous dad.
She tells New York Post gossip column PageSix, "The time has come to now honour my mother by taking her last name from this point on in my life. In the last several months I've come to realise that my father and I just don't see eye to eye on so many things, and I've found I no longer have anything in common with him."
The Men In Black star, 79, hit the headlines earlier this year (10) when he was accused of breaking into a Connecticut bank while drunk and carrying a loaded gun.
He is currently fighting a string of charges, including carrying a firearm while intoxicated, first-degree criminal trespass and third-degree criminal mischief after he was found sprawled on the floor of the Litchfield Bancorp building in the town of Salisbury. He told police he thought the building was his home.
Torn, who has subsequently pleaded not guilty to the counts, voluntarily checked himself into a rehabilitation facility in January (10) after the incident to deal with his alleged alcohol issues.
And he decided to stay away from a bash, thrown by Angelica Torn to celebrate the DVD release of their movie Lucky Days, aboard the vintage Mariner III yacht this week (begs09Aug10) because he feared the sponsorship by Vision Vodka would threaten his attempts to stay sober.
And his daughter, from his marriage to his second wife, late actress Geraldine Page, is fully supportive of his efforts, reports the New York Post's gossip column Page Six.
Angelica says, "He didn't want to put himself in that position, which we all respect."
Rip Torn is facing a mandatory minimum sentence of one year behind bars if he is found guilty for one of the more serious gun charges.
The case is due to go to trial later this year (10).
The Men In Black star, real name Elmore Rual Torn, was detained after police allegedly found him sprawled out on the floor of the Litchfield Bancorp building clutching a loaded revolver.
Torn was charged with carrying a pistol without a permit, carrying a firearm while intoxicated, first-degree burglary, first-degree criminal trespass and third-degree criminal mischief, and was reportedly two-and-a-half times over the legal alcohol limit at the time of his arrest.
He appeared before a judge on Monday (01Feb10) and posted $100,000 (£62,500) bail, but did not enter a plea.
Now, Torn's daughter Angelica has revealed her dad's battle with alcohol abuse, admitting she finds his addiction "heartbreaking".
She says, "My father is a brilliant man, but so much has been wasted. He's p**sed away so much - so much of his time and so much of his talent."
The actor has checked himself into an alcohol treatment centre in New York in an effort to kick his addictions before he heads back to court on 17 February (10).
Torn has previously been in trouble with the law over alcohol-related offences, including a driving under the influence (DUI) arrest in December 2008. On that occasion, he was handed probation and ordered to enrol in an alcohol education program.