In 2019 the Icelandic parliament passed a law on gender self-determination which had immediate consequences for personal name law. It rendered void the clause in the 1996 personal name law that specified that a boy should be given a masculine name and a girl a feminine one. It also introduced a neuter option –bur ‘child’ for parentonyms alongside –son ‘son’ and –dóttir ‘daughter’. This development is part of a pattern of increasing visibility for trans* and non-binary identities. It connects to a long-running discourse on the unpopular personal name law and involves reframing of some earlier disputes, including the case of Blær Bjarkardóttir Rúnarsdóttir, a 15-year-old girl who in 2013, following a lawsuit, was granted the right to bear the name Blær, which had previously been permitted only as a masculine name. Blær’s case was not framed in terms of trans* issues, but the name has later been cited as a precedent for gender-neutral Icelandic names. The declension of such names tends to be unstable and creates new inflectional classes. Expert opinions vary as to how likely it is that inflectional innovations that appear in names will affect other parts of the language. The emergence of new naming practices raises questions about the relationship between gender as an inflectional and as a social category, the future of the inflectional system, and the legal status of grammatical categories.