Renegade Doppelganger

If multiple creatures enter under your control at the same time, Renegade Doppelganger's ability will trigger once for each of them. You choose the order that those abilities will resolve. It's possible to have Renegade Doppelganger become a copy of something, activate an activated ability of that creature, then have it become a copy of something else under this scenario. The last ability that resolves that you choose to use determines what it ends up a copy of.

If a creature enters under your control and Renegade Doppelganger's ability triggers, it can become a copy of that creature when the ability resolves even if that creature has left the battlefield by then. If it has, its last existence on the battlefield is checked to see what it was (specifically, if it was itself or if it was copying something else).

Noncopy effects that have already applied to Renegade Doppelganger will continue to apply to it after it becomes a copy of something else. For example, if Giant Growth had given it +3/+3 earlier in the turn, then it becomes a copy of Runeclaw Bear (a 2/2 creature), it will be a 5/5 Runeclaw Bear.