It would be bad design to tie blocks to character names (1). The block should be tied to an account (or at least characters, not names). I'm not sure if blocks work that way in this game, though, I haven't tested it yet. However, I do believe adding friends is account based.
(1) For example, if you change your character name, and someone else takes this name later on, a character name block would then block this other player. And this doesn't make sense, so blocks should at least be tied to characters (but preferably accounts), not names.