You still call the period before when the sun is directly overhead “morning” and the period after “afternoon” and similarly with “evening”, “night”, “dawn”, “noon”, “midnight” etc.
Note that the Sun position is not consistent throught the year and varies widely based on your latitude.
In Iceland (and also Alaska) you can have the Sun for a full 24 hours in the sky (they call it “midnight sun”) during Summer solstice (with extremelly short nights the whole summer) and the opposite happens in Winter, with long periods of night time.
I think it still makes the most sense to decide that the days of the week (“Monday”, “Tuesday”, etc) last from whatever time “midnight” is locally to the following midnight, again probably rounding to the nearest whole hour.
Just the days of the week? you mean that 2024-06-30 23:59 and 2024-07-01 00:01 can both be the same weekday and at the same time be different days? Would the definition of “day” be different based on whether you are talking about “day of the week” vs “universal day”?
Nope.
https://english.almayadeen.net/news/politics/spain-demands-eu-to-forge-china-policy-without-us--ft
https://news-pravda.com/world/2025/02/24/1082843.html