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I searched the internet for an answer. Finding a satisfactory answer, and ruling out red herrings, will take more time than I am willing to invest. The best I found appears on a 2003 page [1].
The author appears to be Libbie Payne. One story is that hunters searching for Fresh Pond "spied" the body of water of this inquiry and it became known as Spy Pond. She concludes the name was used as early as 1656: An original source notes that Edward Ross, a servant of Edward Winship, "had liberty to mow the grass in the swamp assent to the north end of Spy Pond." She adds an anecdote: An elderly woman [Wikipedia names as Mother Batherick, but the connection is tenuous] gathering daisies alerted the authorities to six Red Coats, surely British spies, making a break for it along the banks of the pond. But that conflicts with her research dating the name over a century before.
Honorable mention to Reddit, where the boston.com page is used to answer the question [2].