建国記念の日 BUT 憲法記念日
In the names of almost all Japanese national holidays we can see の日 （成人の日、春分の日、昭和の日, etc.).
Why is 憲法記念日 different?
記念日 is a common set phrase which refers to "anniversary", or the day when a certain event actually happened, e.g., 結婚記念日, 終戦記念日, 開港記念日. The promulgation of the current Constitution happened precisely on May 3, 1947, so it's safe to call it 憲法記念日.
However, most Japanese national holidays are not associated with actual historical events or events whose date can be reliably determined. 建国記念の日 (February 11) is usually translated as "National Foundation Day", but this date is not reliable because it is based on the ancient Japanese mythology and lot of calculations. The situation is different from American 独立記念日 (precisely July 4, 1776).
～の日 and ～記念の日 are naming conventions that allow people to establish a "memorial/celebration day" with an arbitrary date by avoiding the nuance of "n-th anniversary". To take another example, 成人の日 ("Coming of Age Day", second Monday of January) is associated with no particular historical event. It is not called 成人記念日 because 成人記念日 would sound like someone's birthday. Another example is ポッキーの日 which was determined merely because the appearance of the number
1111 resembles four pieces of Pocky.