Mr. Jonasson has confirmed that the case will not be appealed to the Supreme Court.
"We will revise the naming laws with the aim of seeing if they are out dated", he said.
Ms. Björk Eiðsdóttir, sued the State on behalf of her daughter, Blær Bjarkardottir. Her name was never accepted by Icelandic authorities and was only considered to be a man's name.
Blaer was happy with the decision of the Minister not to appeal and now will finally get a passport with her name in it.