The man who brought the hashtag to Twitter did not name it, and Twitter at first did not want it.
On August 23, 2007, Chris Messina, an open-source advocate, posted a suggestion: "how do you feel about using # (pound) for groups. As in #barcamp [msg]?" He borrowed the idea from Internet Relay Chat, where # had marked chat channels since around 1988. Smithsonian magazine reports that Twitter told him "these things are for nerds."
The word came a couple of days later. The writer Stowe Boyd backed the idea in a blog post titled "Hash Tags = Twitter Groupings." Wikipedia, citing the lexicographer Ben Zimmer, dates it to August 26, 2007. Smithsonian gives August 25. Either way, Boyd is the first known user of the term.
Users adopted the tags anyway. During the San Diego County wildfires that fall, people used #sandiegofire to follow updates. Twitter gave in. From July 2, 2009, it turned hashtags into clickable links to search results. The Oxford English Dictionary added the word in June 2014.
The two halves are older. "Tag" is a label. "Hash" is a name for the # sign, mostly British and Australian. Merriam-Webster says it is short for "hash mark" and probably an alteration of "hatch," the lines artists draw to shade a picture. The sign's crossed strokes look like cross-hatching.
The symbol itself goes back to a Latin abbreviation. Wikipedia traces it to lb, short for libra pondo, "a pound by weight." Scribes drew a line across the letters to mark the abbreviation, and fast handwriting wore it down to crossed strokes. That is why Americans call it the pound sign, a use recorded from 1932.
It also has a joke name. Bell Labs staff adding new keys to push-button telephones needed a word for it, and had "octothorpe" by 1968. The "octo" is for its eight points. Nobody is sure about "thorpe." One story links it to the athlete Jim Thorpe, while another says it was picked because it sounded vaguely Greek.
So a hashtag is a 2007 word for a Latin abbreviation, named after an artist's shading.