FSC said it became concerned about public confusion about the schemes and realised its name lacked the "gravitas or mana" that "Ombudsman" conveys.
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After Wakem declined FSC's proposed name change, the company sought a judicial review.
It alleges her refusal is unlawful, unfair and unreasonable.
Wakem, in turn, applied to have this challenge thrown out by a High Court judge.
She argued a section of the Ombudsmen Act gave her immunity from judicial review.
However, Justice Kit Toogood did not consider her refusal over the name fell within the relevant part of the law.
He dismissed Wakem's strike out bid last month.
It was not plain and obvious, the judge said, that FSC's judicial review bid could not succeed at trial.