A B737-800 air carrier pilot reported a main hydraulic system failure and compounding communication problems with Dispatch while in cruise flight.

Narrative

During cruise we had a Eng 2 hydraulic pump low pressure light. We executed the QRH procedure and continued. About 20 minutes later we lost all hydraulic fluid and pressure on the Hydraulic B side. We executed the QRH procedure up until the deferred items. We tried coordinating with Dispatch but both ACARS and the crew phone were boot working. We were finally able to patch a phone call through a FSS where we spoke with our Dispatcher and informed them of what we had. We came up with the plan to continue to ZZZ and [notify ATC] in order to get priority handling and extended vectors on the longest runway. We coordinated with Approach and informed them we would be exiting the runway upon landing and would like emergency services to look over the plane before we taxied to the gate. We had an uneventful landing and exiting the runway. The firetrucks informed us that our #2 engine was heavily leaking a fluid and recommended we shut that engine down. We shut the engine down and after they confirmed that the leak stopped we taxied to our gate and had them follow us. We arrived at the gate with no issues.Cause: The plane had come out of the hanger in ZZZ1 and hydraulic B had a RF which we had Maintenance come out and refill. This probably should have been investigated further by Maintenance since it had just come out of maintenance servicing.