You'll find that a lot of things probably went over your head reading the books the first time through, the books are just so dense and intricately layered that it's impossible to make all the connections the first time through. For example, remember when Jaqen H'gar somehow magically killed one of Arya's targets in Harrenhal by having the target's dog kill him. Everyone found it strange that the dog became violent towards the man since he raised it from a pup and even Arya mentions that it must have been some dark magic that Jaqen used to do that. Well, remember two or so books later when Arya is being instructed on poisons in the House of Black and White? One of the poisons the waif explains to Arya is Basilisk Blood which she states will produce a violent madness in its victims, including animals, a mouse will attack a lion I believe is the example she uses. Arya then asks if it would work on a dog, the waif replies any animal. Thus, Jaqen used the poison on the dog to kill the man.
Sticking with the Faceless Men, remember when Arya is sailing to Braavos and she mentions how all the crew would present her with gifts and repeat their name, particularly stressing that she knew their name? Okay, well later on when Arya is serving for the Faceless Men when they hold a meeting they begin to discuss targets with one another with one stating, "I know this man, I cannot give him the gift." While another states, "I do not know this man, I will give him the gift." Thus, the implication seems to be that Faceless Men cannot kill people that they know and the reason the sailors gave Arya those gifts and made her learn their names was so that she couldnt kill them later if offered a contract against them.
