Do I need to drain all of the coolant out of the truck?

If the only item you changed was the reservoir, then no you don't need to drain the system. Just add new coolant to it until it hits the full cold mark, Now start the engine and let it run until it reaches full operating temperature and look at the coolant level, it should be at full hot. While it is warming up you might see some air bubbles if the coolant was low for a while from a damaged reservoir. Let it cool back down and check the level again. Top up as needed if it's low. Don't open it while the engine is hot as the system is under pressure and you could get sprayed with hot coolant.

Here is a video on a different vehicle but basically the same process.

https://youtu.be/4K-OifIw0cM

If you would like to take this opportunity and just change all the coolant out though, that would not hurt.

Here is a guide that will help with this.

https://www.2carpros.com/articles/coolant-flush-and-refill-all-cars

Please run through this material and let us know if you have other questions. Thanks