That is, is there a word for the 24-hour period starting at midnight?
I know that technically a day means either 24 hours or the period of time between sunrise and sunset, and that day and night would be specifically 24 hours. A sidereal day is approximately a little less than 24 hours, and a nychthemeron is 24 hours – though it can start at any time.
Is there an equivalent of nychthemeron that specifically starts at midnight?