Agent 355 was a member of a spy group during the American Revolution known as the Culper Ring. The ring worked from 1778 to 1780 around the North United States, in New York and Connecticut, providing important information to General Washington in the fight against the British.
355 was a number code developed by Benjamin Tallmadge, George Washington’s intelligence chief. It meant 'lady'. So we know that Agent 355 was female but with minimal references we don't actually know who she was. The Culper Ring was very successful and had some ingenious ways of communicating. They were also very secretive - even Washington didn't know who all the spies were.
Another female spy in the ring was Anna Smith Strong (although... some think she may have been Agent 355 and there was just a mistake in one of the letters that made 355 appear to be a different person!). Anyway... she developed a method for passing information using her laundry! When she hung a black petticoat out with handkerchiefs, it signalled that a message was hidden in one of six locations. The number/layout of the handkerchiefs showed to her colleagues which location the message was left in. Apparently this sneaky way of getting a message across was never broken throughout the whole Revolution! I'm going to be suspicious of all my neighbours now :-P
Suggest more info could be found in Washington's Spies: The Story of America's First Spy Ring. Alexander Rose. Bantam Books, 2007 - but I haven't got a copy. Definitely could dive into this more deeply and I'm sure there are tons more quite interesting facts about this spy ring, and spies in general, but just an insight for now!