The trivial name carbyne is the preferred IUPAC name. 
Following the substitutive nomenclature, the molecule is viewed as methane with three hydrogen atoms removed, yielding the systematic name "methylidyne".
Following the additive nomenclature, the molecule is viewed as a hydrogen atom bonded to a carbon atom, yielding the name "hydridocarbon".  
By default, these names pay no regard to the excitation state of the molecule. When that attribute is considered, the states with one unpaired electron are named "methylylidene" or "hydridocarbon(•)", whereas the excited states with three unpaired electrons are named "methanetriyl" or "hydridocarbon(3•)".