Since the player's name / id is public - which previously, before the implementation of the lobby, was the account's username / id - it has the same value (as an information) with the new account username / id. So, there is no "data protection" issue here, at-least in my opinion. I guess admins have access to such information, but I do not know if they signed any confidentiality agreement during their hiring process.
Should the main account's id be visible? Probably no ... From the one hand (the bad side), some people may try to find out how many players one person controls (which is none of your business), so that they can harass players by attacking their lower level accounts. On the other hand (the good side), it would open more possibilities, like account messages inbox, account friends, etc.