The Romans kept guard geese on the Capitoline Hill. This came in useful when Rome was attacked by the Gauls in 390 BC, so useful in fact that the Romans put up a temple in thanksgiving. But being ungrateful sods they didn’t dedicate it to geese, they dedicated it to Juno, the goddess of warnings, or Juno Moneta.
Next door to the temple of Juno Moneta was the building where all the Roman coins were produced. In fact, the coins may have been made in part of the temple itself. Nobody is quite sure, and the sources are rather vague. What is certain is that the coin-producing building got named after the temple. It was the Moneta, and though we’ve changed all the vowels, we still call such a building a mint.