In 2013, Björk and Blær won a court case for the right to use this name—see also Icelandic Naming Committee#Blær Bjarkardóttir Rúnarsdóttir
Björk and Blær successfully defended their right to use the name in 2013, as documented by the Icelandic Naming Committee#Blær Bjarkardóttir Rúnarsdóttir.