"getting what our name is" - to me this means that a relationship which lacks depth, one in which you leave behind the heaviness you normally would carry with you, you leave with the "same as what you came with" meaning you approach the depth of a meaningful relationship but then leave it behind--that, in the end, this kind of relationship really does leave both parties with nothing. their name is nothing, they don't label themselves or their status, and they end up with empty hands at the end--perhaps without broken hearts as well.
"getting what our name is" - to me this means that a relationship which lacks depth, one in which you leave behind the heaviness you normally would carry with you, you leave with the "same as what you came with" meaning you approach the depth of a meaningful relationship but then leave it behind--that, in the end, this kind of relationship really does leave both parties with nothing. their name is nothing, they don't label themselves or their status, and they end up with empty hands at the end--perhaps without broken hearts as well.