New Mexico State Police say the victim was 30-year-old Stuart Gordon of Lincoln.
His name was released Wednesday after his relatives were notified of his death.
State Police say 39-year-old Jo Hill is jailed without bond on suspicion of an open count of murder.
The Magdalena Marshals Office was dispatched Monday afternoon to the High Country Lodge about a gunshot victim.
Gordon was pronounced dead at the scene and State Police was brought in to investigate.
They say Hill and Gordon got into a physical altercation in the parking lot of the lodge.
Hill then reportedly shot the victim.
It was unclear Wednesday if Hill has a lawyer yet.