Senators Nick Xenophon and Skye Kakoschke-Moore of the Nick Xenophon Team have raised the idea of dropping the age-restrictive word "Children's" from the name of the Office of the Children's eSafety Commissioner.
Speaking in Senate Estimates, Xenophon said the word may stop young people, particularly those affected by revenge porn, from seeking out the office for help.
The idea was not dismissed by Communications Minister Mitch Fifield.
"It's something that is in my mind. The role of the Office of the Children's eSafety Commissioner is one that has expanded over time," he said. "I think that's a good thing, you raise a pertinent point in terms of how the office is branded and what people might think that means in terms of the range of advice that is available."
The minister said no decision had been made, but he was mindful of it.
"I just myself [am] increasingly referring to 'The eSafety Commissioner' in those terms," he said.
Last week, the office said it responded to 70 serious cyberbullying complaints in the three months to September 2016, representing a 75 increase over the same period last year.
The Office of the Children's eSafety Commissioner was established in July 2015 and has the power to fine social media companies for not removing content deemed to be of a bullying, offensive, or illegal nature.