The name promises "equal night," and the day itself does not quite deliver it.
Equinox comes from Latin aequinoctium, joining aequus, "equal," and nox, "night." Medieval Latin had equinoxium, "equality of night (and day)," and Old French had equinoce from the 1100s. Etymonline says English took the word around 1400, either from the French or straight from Medieval Latin. Its first English definition already named the astronomy: the point when the sun crosses the equator, making day and night equal everywhere.
English had its own word for this before the Latin one arrived. Old English translated it as efnniht, literally "even night." The native word faded, and the borrowed one stayed.
Both halves of the Latin have long families. Etymonline describes aequus as being of unknown origin, but it also gave Latin aequalis and English equal. Nox goes back to an Indo-European root for night that also produced Greek nyx and English night itself. So the Old English and Latin terms were built the same way, and their second halves are true cousins.
Astronomically, an equinox happens when the center of the sun's disc crosses Earth's equator. Because Earth's axis is tilted, this happens twice a year: around 20 March and around 22 or 23 September. On those dates the sun sits directly over the equator.
Yet the "equal night" in the name is only approximate. In an analysis for UCL and The Conversation, Osnat Katz explains two reasons. Sunrise and sunset are measured from the sun's upper edge, not its center, which adds daylight at both ends. The atmosphere also bends sunlight, so we see the sun for several minutes before it actually clears the horizon.
The result is that day runs a little longer than night on the equinox itself. The date when the two really match is called the equilux. It falls a few days away from the equinox and shifts with latitude. Katz gives 17 March as the UK's equilux in 2021.
The word survived the correction. "Equal night" was close enough for the Romans, and it has been close enough ever since.