Mmm. Hard to say. I seem to recall someone stating that, stricitly speaking, a major ship like a carrier ought to be named after the monarch - the CVA 01 was meant to be called the Queen Elizabeth; CVA 02 would have been the Duke of Edinburgh (although some sources say that this is speculation, I've seen the minutes of the Admiralty meeting that decided this).
The current Ark was meant to be called Indomitable but was renamed partly as a result of public opinion after the Sailor programme; I guess that the name might be in with a chance. Traditional carrier names like Hermes and Eagle ought to be possibilities, and - bluff old traditionalist that I am - I'd like to think that Furious , Courageous and Glorious would at least get considered.
However, as long as we don't get some attempt at pandering to popular sentiment with HMS Posh and HMS Becks...