Why did we choose "Lilius" as a calendar name? Only because it is a short and memorable word?

Well, that's a reason too, but there is a story behind it as well.

There is no more "calendarish" name than Lilius. Aloysius Lilius (c. 1510 – 1576) was an Italian doctor, astronomer, mathematician, and also the primary author of the new reformed Gregorian calendar that was adopted in 1582 by order of the Pope Gregory (that's why it is called Gregorian) to fix the accumulated error of 10 days of old Julian calendar.