Half-Life 3 has been removed as a registrant in the Trademarks and Design Registration Office of the European Union (OHIM).
Searching for the registry number at the OHIM will find it doesn't exist anymore, but all of this doesn't explain the numerous Half-Life 3 references, images and logos that appeared in Valve's internal groups, as seen below.
It seems like either an external party committed a hoax, or Valve prematurely registered Half-Life 3 while it's still in development.
Adding to the intrigue, an OHIM registry for Portal 3 has appeared, and this entry was vetted by OHIM itself, meaning it's confirmed.
Half-Life 3 removed from trademark registery - Portal 3 appears
05 October 2013 | By JonahFalcon