Deadlifts will hit most of the posterior chain, but to really grow thickness in the upper and mid back you'd need to add in heavy rows and/or pull-ups as OP mentioned.
Might as well chime in with the basic back-of-a-napkin strength program -> One movement for: (1) vertical push, (2) vertical pull, (3) horizontal push, (4) horizontal pull, (5) glutes/"back of your legs", (6) quadriceps/"front of your legs".
To beat the dead horse, deadlifts definitely involve pulling but it's primarily a glutes exercise. Adding in dedicated pulls like pullups and rows will give you a lot of bang for your buck.
Well, if we're all chiming in: another requirement is a caloric surplus. Beginner gains are a real thing, but at a certain point (say 8-10 weeks) a caloric surplus will be required to continue seeing changes in strength and muscle mass. And that reminds me, the weights also need to get incrementally heavier.
