Laws was off-air from his RadioLive show at the time, after saying journalists should be shot for their "rabid" coverage of the John Key-John Banks teapot tape during the election.
In court, Stephen Ross, acting for Brookhammer, argued that she should get name suppression on the grounds there was "minimal" public interest in her compared to the public interest in her victim (also a former MP and Mayor of Wanganui).
The matter was minor and she was "trying to live a normal life" after being in a position where her every move was followed and highlighted by the press, he said.
Mr Ross said the objective of diversion was to allow a person with a good record and good character to avoid a conviction, and to name her would endanger that objective.
Brookhammer wrote to the court arguing she should be granted name suppression on the basis that publicity about the case would have an adverse impact on her, outweighing the interests of justice.
Judge Cameron disagreed. He said diversion was not a reason for granting name suppression, there was a public interest in the case and the court must ensure its processes were open in the interests of justice.
Brookhammer had a turbulent relationship with Laws.
She appeared in a women's magazine less than a year ago talking about their break-up and introducing her new partner, 15 years her junior.
In 2010, she made headlines after revealing, again in a women's magazine, that she used to punch Laws in the face and became an alcoholic during the breakdown of their relationship.
