Marshal with one L is the rank and the verb — a field marshal, marshal your arguments. Marshall with two is normally a proper noun: a surname, or names like the Marshall Plan and the Marshall Islands. The common noun takes one L.
The core difference
A common noun and verb, and a proper noun.
- marshal — an officer or official; to arrange: fire marshal, marshal the evidence.
- Marshall — a surname or place name: the Marshall Plan.
The verb
Marshal as a verb means to gather and arrange in order — marshalling facts, marshalling troops. It doubles the L in British inflections: marshalled, marshalling. American English keeps the single L: marshaled.
The martial trap
Marshal and martial are separate words too — martial means relating to war. "Marshal law" is an error for martial law, and it is a common one.