The RHS is the International Registration Authority for Dianthus, including all types of carnations and pinks. A list of cultivar names was published in The International Dianthus Register, and it is kept up-to-date with regular supplements. As well as names, these publications include wherever possible a brief description, parentage, date of raising and classification for each cultivar.
Download registration forms here:
Application form to register a Dianthus cultivar name
The RHS publishes a list of cultivar names in The International Dianthus Register 1982 (now out of print) and subsequent supplements, some of which are available as downloads from the link below.