From U.S. capture to 1974, I would go with the U.S. government designation.
Eniwetok Atoll, Marshall Islands, United States of America.
In the biography, I would add (now Enewetak).
Rālik Chain is the legislative district which might be their equivalent of county, if so it would go after the island name and before the territory. I believe the Marshalls only have two legislative districts.