I know that AM/PM is for ante/post meridiem, but what is it actually called? Meridian indicator? 12 hour indicator? Something way more clever?
The Unicode standard for date/time formatting calls it "period".
Wikipedia says: The 12-hour clock is a time conversion convention in which the 24 hours of the day are divided into two periods
Ruby documentation (and probably a lot of strftime references) seems to refer them as "Meridiem Indicator".
From a user interface perspective, a "Period" label is too ambiguous, and "Meridiem Indicator" too pedantic, still leaving "AM/PM" as the best choice.
As for the actual meanings of AM/PM, they come from the Latin "ante meridiem" ("before noon") and "post meridiem" ("after noon").