Air carrier Captain reported the First Officer descended below the desired vertical path on approach to RAP when he mistakenly identified RCA airport as RAP.

Narrative

Flying into RAP ATC cut us in for a tight visual approach to 14 due to two aircraft coming in behind us. We had set up for the RNAV; and elected to take the visual rather than a potentially extensive delay. The FO was flying; once cleared for the visual approach the FO vectored himself further down wind and outside of the final approach fix to set himself up for a better turn onto final. In his turn he began descending and configuring for the visual approach. Coming out of his turn he mistook Ellsworth AFB for RAP; stated that he was a bit high and initiated a descent to try and correct the issue. As PM I recognized the error and called out that he was attempting to descend for the incorrect runway and pointed out the correct airport. He stopped his descent and leveled off at 4500 MSL. At this point he was Gear Down with Flaps 30. FAF required altitude was 4900 feet. As we continued level towards the FAF the aircraft called out 1000 feet. I never observed the RA showing less than 1000 feet so I allowed him to continue. Shortly after the 1000 feet callout the RA showed an altitude gain of 2-400 feet. He continued on to a stable approach to landing. We debriefed the approach and the issues with it after shutdown.Cause: Time pressure; Company performance pressures; followed by a break down in situational awareness by the pilot flying.