Destiny 2 will not have ranked PvP at launch. The news was confirmed by game director Luke Smith in a recent interview with PC Gamer.
"There is not going to be a ranking system for the September launch," he confirmed. When asked if the feature might come in a post-launch update though, he was non-committal: “I anticipate things like ranking systems are going to be very desired, and we’re going to have those conversations. But I’m not going to commit us to any of that work on the phone.”
There may be other elements of prestige for successful competitors though. Speaking on Kotaku's E3 2017 podcast, he teased there would be “some other ways for players to show off their prowess to other people”.
So, there definitely won’t be ranked PvP on launch day, but it does sound as though Bungie will reward players with some content (probably cosmetics) for putting time and effort into the Crucible.