"No one should be allowed to make money on our daughter's death, and we would rather not have her name on a memorial," Vanessa Svebakk told Norway's NRK television channel.
Svebakk's daughter Sharidyn was shot in the chest as she tried to escape the killer after he unleashed his gun massacre the island of Utøya. She died almost instantly.
Dahlberg's design for two permanent memorials to the dead was chosen at the end of last month by Koro, the body which commissions public art in Norway, and has been praised worldwide for its poignancy and imaginativeness.
He aims to carve a three-and-a-half-meter wide slice through Sørbråten, the peninsular which juts out into the Tyrifjorden towards the island, to create a permanent scar on the landscape.
The names of the dead will be carved on one exposed surface, which will be viewable to visitors who come down an underground walkway.
"We have never been asked for permission to use our daughter's name on a memorial," Svebakken objected. "We see it as state overreach and undemocratic."
Svein Bjørkås, who heads Koro told NRK that this was the first time he had heard that any of the bereaved objected to the memorial.
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He conceded, however, that Koro had not directly contacted all of the bereaved relatives of the 77 dead, and had instead shared information through intermediary organisations such as the AUF, the labour youth group that runs the summer youth camp Breivik attacked.
"It's a whole new problem. We will examine what we can and can not do," he said.