A popular and apocryphal story of how the town got its name in 1887 is one based on a misunderstanding. When the townsfolk were completing the government application to establish a post office, they interpreted the instruction "Write in ink" literally and entered the name "Ink" as the proposed town name. This was accepted as the official name.
The true story is that many towns were trying to register at the same time, and the United States Postal Service was trying very hard to limit the number of duplicate place names. Post Masters of the various post offices trying to register their towns were required to give several name alternatives. Most towns did not get their first, second, or even third choices. Ink was actually the second choice, the first being "Melon".
Ink has been noted for its unusual place name.