Does the ICZN govern common (vernacular) names?

No, only scientific names are covered by the ICZN. Common names may be standardised within particular regions or for particular taxonomic groups, but there is no international standardization. There are a few projects that are aiming to bring together scientific and common names such as the Pan-European Species Infrastructure (http://www.eu-nomen.eu/pesi/) or FishBase (www.fishbase.org/), but these are databasing projects and do not include a regulatory process.

Scratchpads developed and conceived by (alphabetical): Ed Baker, Katherine Bouton Alice Heaton Dimitris Koureas, Laurence Livermore, Dave Roberts, Simon Rycroft, Ben Scott, Vince Smith