Young Metallica's battle has attracted attention from around the world, and has prevented the family from travelling - the youngster has been unable to get a passport before the dispute was solved.
"It feels good," Metallica's mother told Göteborgs-Posten on Thursday.
The row started when the Swedish Tax Board ruled that Metallica was not appropriate as a name. Officials objected both on the grounds that it is the name of a heavy metal band and that it is too closely related to the word 'metal'.
The girl's mother, Karolina Tomaro, took the case to the County Court, where she secured a victory over the tax authority. Officials then vowed to appeal the decision. On Thursday, however, the tax board said it was dropping its appeal, allowing young Metallica to keep her name.
The media attention given to the battle has led to Tomaro, from Kungälv, near Gothenburg, receiving support from people around the world.
"Several people suggested I should move to where they live, because then our daughter wouldn't have any problem in being named Metallica," she told Göteborgs-Posten.