Zayn Malik and Harry Styles told an interviewer in Australia that they were determined to retain the name that they adopted when taking part in the 2010 series of The X Factor.
The interviewer for the Herald Sun asked if they would have to change their name, to which Zayn replied: "No."
Asked if that was an official "no", Zayn looked at Harry and answered "yes".
Harry then chimed in to say: "We don't know. No. We will not be changing our name."
And when asked what would happen, Zayn continued: "We don't know, but we're not changing our name."
The US group registered the name as a trademark at the start of 2011, but claim to have been recording under that name since 2009.
In other One Direction news, Harry was more tight-lipped when quizzed about texting American country pop superstar Taylor Swift.
He confirmed he'd been in touch, but would only say: "We met in America and she's very nice."
Earlier this week we told you how the boys were reported to have been paid £10m by Simon Cowell.
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