B737-800 Captain reported experiencing a phugoid oscillation due to stabilizer trim malfunction.

Narrative

After the after take off checklist was completed; autopilot B was engaged. A bump that felt like a small wake turbulence encounter was felt. The yoke also lurched. A divergent phugoid was then encountered. It was initially noticed by continuous and reversing trim wheel movement. The aircraft was unable to maintain commanded speed or an appropriate pitch. The autopilot was disengaged. After a proper hands off trim was set; command B was reengaged. We thought that phugoid was a result of hitting aircraft wake. The process then repeated. The stab out of trim light illuminated. At that time we then advised ATC for a flight control malfunction and returned to ZZZ. Approach control asked if we could accelerate to 300 knots. I said negative and thought to myself are they idiots; I just told them I had a trim and horizontal stab issue. I asked for the emergency equipment to be present for landing. The FO who was pilot flying continued to hand fly the aircraft to landing. We completed all appropriate checklists. On the threat forward brief we discussed what might happen to required trim after selecting a new flap setting. We had and maintained positive communications that verified what each of us was about to do. Also in the fuel and souls on board we also mentioned that we had a dog in the forward cargo.Great CRM mitigated risk.