Based on the information I can find about the naming process and the fact that all articles related to the naming date from 2010/2011 this implies to me that the name was chosen and finalized in the months prior and regardless it was named under Obama because his SECNAVY made the name official if the name had been chosen years in advance it makes little difference as the SECNAVY at the time of handing out the contract the building of the vessel is the one who makes the name official.
Also if Bush wanted a vessel named after Chavez during his time he had would have named a vessel that would have been launched while he was in office(some only take a year or so clearly) if he wished to receive any political gain this would have to have been long ago during his first term. Obama gains from this naming that is very clear the ship gets launched in 2012 in San Diego no less and is named after a person prominent to many Hispanics.
