As part of its blog post, Bungie explains that Destiny 2 players on PlayStation, Xbox, PC and Stadia will be able to join, or face, each other in games. The developer also explains a number of changes to the game that will happen as part of the process.  

One is the way player names will be displayed. The developer calls this the players’ Bungie name, the implementation of which will cause a one-time naming reshuffle. But beyond that, Destiny 2 players will be identified by their name, a numeric ID, and the platform they are currently playing on. You’ll also see most of this in the roster screen, so you’ll know which platform your teammate is playing on when you invite someone. Things will remain largely unchanged on the friends and clan front. They will all remain, but for clans, you’ll be able to see everyone that’s online, not just those that are on the same platform as you.

For PvP modes, naturally PC players won’t be matched with console players. Unless you’re playing in a team event and someone on your team is on PC, then you’ll be matched within the PC pool. One major wrinkle in the crossplay rollout for Destiny 2 is that voice chat will not be available at the start. Bungie says it will be added in an update shortly after, so there’s that at least. Though overall, there’s no exact date as to when crossplay goes live for Destiny 2. Bungie says this will all happen as part of Season 15, and an upcoming reveal is scheduled for 24 August. (Source: Bungie)

Bungie Reveals Destiny 2 Crossplay Plans As Part Of Season 15 - 45Bungie Reveals Destiny 2 Crossplay Plans As Part Of Season 15 - 7