Bungie, makers of Destiny, have filed three trademarks with each of them are related to “Eververse”. The trademarks Bungie have filed for Eververse, Eververse Trading Co., and a logo for Eververse (seen below).
Since the term “Trading” is in one of the trademarks titles, I can’t help but think that this might be a hint at in-game trading for Destiny players. A lot of Destiny players have been asking for a trading system like World of Warcraft or Diablo, which could work out for both people in the trade.
Whatever Eververse is, it’ll most likely show up in the next DLC that Bungie is likely to show off at E3 in a few weeks, which according to a trademarked filed a few weeks ago will be called The Taken King.