Earth’s moon is notably big. Relative to the size of its parent planet, it’s easily the biggest* in the solar system (or second biggest if you Stan Pluto as a planet). If there was a second moon, it would likely be a lot smaller. So, I don’t think it would have much practical effect on things like tides or timekeeping. It would still have cultural significance in things like mythology and astrology. If we could observe moon-moon interactions we might have discovered gravity earlier.

/* in absolute size, there are a couple of larger moons, but they’re moons of giant planets so Luna still wins in relative size.