Are you playing as William? Since Desmond is probably dead and William obviously has the same ancestors (unless Connor is an ancestor of Desmond's mom) , it seems the most probable reason you can still play as Connor.
Also, is there a way to replay the Desmond missions after you finish the game?
The strategy guide says the voice at the end is from a Templar agent, possibly from Abstergo. Erudito was my original guess too. Maybe Erudito is an ex-Templar who defected over to the assassins or maybe an ex-Templar who is now a neutral third party. IDK, we will have to wait for the next installment.