Interestingly enough, not Galileo. There was a man named Simon Marius who also discovered the moons of Jupiter through his telescope, one day after Galelio.
Despite the closeness of the discovery, Galileo got the credit because he published his findings in 1610, whereas Marius didn’t publish his findings until 1614.
Although, this oversight is eased a bit by the fact that Galileo was technically the first. The names for the moons: Ganymede, IO, Callisto, and Europa came from Marius’ work. So, one gets the credit, and the other got to name them.