No, the XBox live logo is always included whenever live can be used with or on a game, etc.
PSN does not exist anymore, folks. It's SEN that has taken it's place. Besides, do you know the amount of confusion there would be if the next console was called xbox live? it would be lower than idiotic to have such a name. I'd trust an 8 year old to come up with something better.
Don't be silly.
Need I finally say, SEN can be accessed on a number of consoles, meanwhile, Xbox live can only basically be accessed from a PC and 360, for the most part. Whatever the case, the name of the new console wouldn't be a service that's still current. That's stupid. I'm sure developers would pressure microsoft to call it something different.