Yahtzee's name looks like a made-up word because it is one, and the person who made it up left no explanation that I could find.
Here is the part the sources agree on. According to Hasbro, the game's current owner, an anonymous Canadian couple invented it and called it "The Yacht Game," since they played it with friends on their yacht. They asked the New York game maker Edwin S. Lowe to produce sets as gifts. Lowe saw the commercial potential and acquired the rights in exchange for 1,000 gift sets.
Lowe renamed it Yahtzee. Wikipedia reports that he filed the trademark on April 19, 1956, a few weeks after the first commercial use on April 3. Toy Tales and the Yahtzee Manifesto both describe the renaming but neither says how he picked the word. The Manifesto says only that the name evolved from "the Yacht Game," likely influenced by "Yatzie," an earlier dice game from 1943. That the word is a respelling of Yacht is a reasonable guess, not a documented fact.
The couple's identity has never been revealed, and nobody has claimed credit for the invention. The game itself was not wholly original. Wikipedia lists earlier dice games as its sources: Yacht, which dates to at least 1938, plus Generala, Poker Dice and Cheerio. It is also close to Yatzy, a game popular in Scandinavia.
Lowe's earlier success helped him here. Toy Tales notes that he had introduced Bingo to the American public. Yahtzee sold slowly at first, because advertising struggled to explain the rules. Lowe then threw Yahtzee parties and word of mouth did the rest. Milton Bradley bought the E.S. Lowe Company, with the rights, in 1973.
None of the pages I opened give a year for the couple's game, so it is left undated here. Only 1956, for the commercial release, is firmly sourced. The Manifesto adds that the trademark was registered on March 19, 1957.