I think crowns (and subs) will not make it to consoles, because players there already have to pay console-specific networking racket and therefore are unable to spend further money on ESO. Which is why compulsory subs were abolished.
Your visible in-game identity will be your XBL Gamertag or PSN ID, which is a standard set by Microsoft/Sony.
Crowns will be on-sale through the XBL Marketplace and PSN Store, along with ESO Plus for those who want it.
Your visible in-game identity will be your XBL Gamertag or PSN ID, which is a standard set by Microsoft/Sony. ZOS may be able to change that in the future, but at the moment they want to remain consistent with other XB1 and PS4 games. Character names I believe will be visible somewhere, but I'm not sure where.