I understand we would all die and this is a common “think about your question before you ask it” thing in high school, but what would we call an eclipse where the Sun gets in between Earth and the Moon?
Solar eclipse comes from Latin solaris, lunar from lunaris, and Terran eclipse (terra) seems like it’s already one of those two from the Moon’s perspective.
Orbital? Terrar? Orbar? Tellar?
The Sun won't pass between the Earth and the Moon in the near future, because the Sun is so much further away from the Earth, than the Moon. When the three are nearly co-linear, either the Earth blocks sunlight to the Moon (a lunar eclipse), or the Moon blocks sunlight to the Earth (a solar eclipse). But just because this is impossible in the near future, doesn't mean it is impossible forever!
Gastineau and Laskar have long term orbital models in which the orbit of Venus expands to reach the Earth. Their paper in Nature is unfortunately behind a paywall, but there is a nice article here, that includes a diagram for a potential orbital scenario of the Solar System in the future.
Here, the green orbit is Earth's path and the blue orbit is Venus's path. I used this as a taking off point for my answer and ran a simulation in which Venus passes close to the Moon and causes the Moon to achieve escape velocity from the Earth. In it's new orbital path, the Moon has a slower orbital period than the Earth, and in less than 10 years is on the opposite side of the Sun from the Earth. As mentioned in the other answer, this would most likely be known as a Solar Occultation, but in the remote possibility that a sentient species was still alive, I imagine they would have a special term for this extraordinary event!
Of course it’s a silly question as stated and you clearly know it. But such things (with bodies other than the sun earth and moon) do exist, where one object passes in front of another from our point of view blocking our view.
They go by the generic name of “occultation”. Solar eclipses are occultation too (the moon is said to be occulting the sun) but they are rarely described with that word.
Lunar eclipses are not occultation (from the point of view of the earth) because it’s “us” blocking the sun from the moon, but our own view is not being blocked. However it would be valid for an astronaut on the face of the moon during a lunar eclipse to say that the earth occulted the sun.
If you think outside the Earth-Moon system, but look at the planetary system as-is now, the planets experience just that what you refer to when looking from Earth. This phenomenon is commonly called conjunction, referring the apparent places of Sun and the planet falling (nearly) into the same place on the celestial sphere (we have to exclude the 'inferior conjunction' for the inner planets where we have Earth-planet-Sun aligned and we only see the dark side of the inner planet; for those we talk about the 'superior conjunction. For the outer planets there can be only one conjuction, thus no distinction is made).
Obviously anything in conjunction is actually either hidden directly behind the Sun, or it is showing the full disc very near the Sun (thus quite bright, but hardly or not seen at all due to the tremendous brightness difference when compared to the Sun adjacent to it).
This said, this phenomenon only makes sense for bodies which orbit the Sun separately as otherwise the Sun will never be between those (and that's even true for any hypothetical worlds one might create). If a star is somewhere on the line between two objects, those two objects MUST be orbiting the star separately and are never a planet-moon system. Any argument with reference to mass also fails as then we would be talking about multi-stellar system, if the masses of the orbiting objects influenced the orbit of the star more than the star them. For multi-stellar system one talks of occultation when one star seemingly hides behind the other.
The alignment of three or more astronomical bodies is referred to as a syzygy, from the Greek "suzugos", meaning "yoked together". Parenthetically, it is also a favorite word for crossword puzzles (helpful hint).
