Learn English – term for the period between midnight and sunrise

Times:

1. Dawn refers to the time around the actual solar event that is sunrise.

2. Morning refers to any time before noon, so 1am is still the morning.

3. Very early morning is sometimes known as "the small hours" (or any regional variant of those words). The actual time is variable, although you will probably provoke a laugh from working people if you refer to any time after 7am in that way (and probably any time after 6am).

4. Noon refers to 12pm (exact midday) and the time just around it. 1101 is not noon.

5. Afternoon refers to the time after Noon and before the Night. "Good afternoon" is only used after noon.

6. Dusk corresponds to dawn, and refers to the event of the sun setting.

7. Evening is variable in its usage, and is tied both to work schedules and the solar time. It's pretty much always correct to refer to the part of the day when the light begins to wane as "evening".

8. Night refers to the time after sunset. Accordingly, it can be both morning and night (this being pretty much the definition of the small hours).

9. Midnight refers to exactly 0000/2400 hours, and the time just around it. 2301 is not midnight.

10. "Good night" does not mean "have a good sleep". It is used as a farewell when it is late, whether anyone is planning on going home or not.

Meals:

1. Lunch is a meal taken between breakfast and the evening meal (howsoever called). It is not tied to any specific time beyond that.

2. The main evening meal may be called "dinner", "supper", or "tea" depending on regional dialect and class. "Dinner" is probably the most neutral option in most dialects (although in some dialects it means the main meal of the day even if that was lunch, or it may mean something else). If a second evening meal is taken, or a very late evening meal is taken, it might be called supper in distinction to dinner. This is not so common any longer.

3. "Afternoon tea" is a specific meal. Its defining feature is not really that it is taken in the afternoon, but rather the elements it is composed of: it will be a short snack, usually of tea or coffee and a sweet or savory baked good. "Morning tea" is the corresponding snack in the morning.

We are not "fixing" you, because you are not broken. We are correcting you in so far as we think you are wrong.

I would say that the periods of a day are simply time periods. For example, the definition of morning time says it is:

the time period between dawn and noon

You could also call them periods. The definition of evening says:

1. The period of decreasing daylight between afternoon and night.
2. The period between sunset or the evening meal and bedtime: a quiet evening at home.
3. A later period or time: in the evening of one's life.

Edit: A more specialized term, used in broadcast programming, is dayparting. That is,

In Broadcast programming, dayparting is the practice of dividing the day into several parts, during each of which a different type of radio programming or television programming apropos for that time is aired. Television programs are most often geared toward a particular demographic, and what the target audience typically engages in at that time. Arbitron, the leading audience measurement ratings service in the United States, divides a weekday into five dayparts: morning drive time (6-10 am), midday (10 am-3 pm), afternoon drive (3-7 pm), evenings (7 pm-12 midnight), and overnight (midnight-6 am; Arbitron generally does not measure during this time period).

You could adopt this term for the use you seek, although many people would not know its precise origin. The individual parts of the day could be termed dayparts.