They do not really make it clear in Bleach, at least not yet how long it is before a shinigami actually sees their avatar. In the case of Ichigo it was in weeks, but he is a special case. I know that the thing with Renji is coming up so I will know better than in his reaction of seeing his and whether he talks to his frequently or not.

But I would think that if you know the name of your Zanpukto you would have had to gain it in some fashion. I guess it could just be a voice, but I'd imagine it would also be through actually speaking to the avatar. I would agree that it is too early to learn the name, however I'm not sure what the problem is with seeing the avatar. I didn't think that seeing the avatar would be something that would take centuries to do. It seems fairly insignificant, but I haven't seen all of Bleach yet so I'm just making that decision off what I know.