Galileo was the first to observed the phases of Venus, also here, which he was able to do by his telescope, around 1610. It was the phases of Venus as well as observing Jupiter's moons orbiting Jupiter, that, to Galileo, confirmed without any question that Copernicus' model was the correct one and planets orbited the sun and moons orbited planets. Galileo's publications of 1613 were banned in 1616 and in 1633 he was put on trial and sentenced to house arrest, narrowly escaping the death penalty. Timeline here.
Francesco Fontana and here, was inspired by Galileo and while he was also an artist and a lawyer, he also constructed his own telescope and extensively observed the moon and planets and he made similar wood carvings of all the known planets and detailed observations of the moon. A crater on the moon is named after him.
That particular drawing, or printing is probably more correct, as it was made from woodcuts, was done in 1646, about 4 years after Galileo's death. It seems to show the phases of Venus as well as a moon or a few moons orbiting Venus. As strange as that picture looks today, it was pretty cutting edge astronomy at the time, and it was (perhaps) still dangerous to make that claim in 1646. I'm not sure of that, but that printing might have been scandalous at the time.
Fontana claimed to have observed a moon around Venus in 1645. Cassini and several others also made that observation, See here. Cassini in 1672, and by that same article, the first recorded observation in 1650, which is a little inconsistent, but in the same time period. It's entirely possible that Fontana observed what he thought was a moon or moons around Venus by telescope.
Neith is a hypothetical natural satellite of Venus reportedly sighted
by Giovanni Cassini in 1672 and by several other astronomers in
following years. The first supposed sighting of this moon was in 1650.
It was 'observed' up to 30 times by astronomers until 1770, when there
were no new sightings and it was not found during the transit of Venus
in 1761 and 1769.8
and a likely explanation for the moon from that same source.
In 1766, the director of the Vienna Observatory speculated that the
observations of the moon were optical illusions. He said: "the bright
image of Venus was reflected in the eye and back into the telescope,
creating a smaller secondary image."