Destiny's next expansion will be called Rise of Iron, according to a leaked poster on Reddit that portrays Lord Saladin brandishing a flaming axe. Bungie will formally announce the DLC at E3 2016, followed by a launch in the month of September.
According to Kotaku, Rise of Iron will include a new Fallen-themed raid, and will be larger that the two DLCs released thus far. We should be hearing more about the expansion next month.
The successor to Destiny was originally slated to launch this fall, but it now looks like we'll be treated to the DLC for the original game instead. As for when Destiny 2 will be available, current estimates suggest an unveil sometime next year.