Final answer:
The name of initial membership in the Order of the Arrow is the Ordeal, representing a challenging initiation phase similar to initiation rites in many cultures, marking a passage and transformation.
Step-by-step explanation:
The initial membership level in the Order of the Arrow is known as the Ordeal. This name represents the challenging initiation phase that new members must undergo to demonstrate their commitment to the ideals of the Order, which includes service to others and dedication to scouting principles. The Ordeal membership serves as an important rite of passage, not unlike various initiation rituals observed in many cultures around the world, where initiates must separate from their normal environment, undergo a period of learning and transformation, and then reintegrate with their community showcasing their new status.