Both Alice and Bob check if a name is already registered beforehand. Lets say that both of them see that a name is available and go to register it at the same time. Either both will fail (due to taking X names each) or one will succeed (per the consensus requirements.) The software will indicate the results by checking the channel owner after registration for each server. So you know whether to try register a different name or not. So conflicts can still happen here but they're reduced by having unique TLDs + names, requiring small computations, and checking availability beforehand.