(and I'm sorry, but what does "naming months and seasons in Mars" have to do with this?)
The first option breaks mostly assumptions made in software and processes, the second mostly assumptions made in hardware, and the third breaks human's circadian rythm (a 23 or 25 hour rythm isn't a big deal, but it has to sync to light).
Of those three, the things that rely on 24 hour days seem to be the easiest to change. Though there is precedent both to messing with the length of a day (a leap second makes the day one second longer, making 23:59:60 a valid time) and the length of a second (google pretends like seconds are slightly longer as an alternative way to deal with leap seconds)
[0] https://gist.github.com/timvisee/fcda9bbdff88d45cc9061606b4b...
23:59:60 happens when we add leap seconds to the clock, for instance...
Round-the-clock shiftwork (hospitals, power plants, etc.) will require minor tweaking; your eight hour shift probably just becomes 8:10 or so.
(It's worse for humans on Earth working Mars time, which is a thing that already happens. They come in 40 mins later every day. https://mars.nasa.gov/resources/20090/living-on-mars-time/)
Daylight savings time is a much larger departure from this rule ;)
> 23:59:60 happens when we add leap seconds to the clock
Not anymore! Or, maybe not anymore. We've agreed to phase out leap seconds before 2035 [1] and we probably won't get a 23:59:60 before then [2].
[1] https://www.nature.com/articles/d41586-022-03783-5
[2] https://manifold.markets/Yev/will-there-be-another-positive-...
I read[0] that "It will take about 50,000 years for a mean solar day to lengthen by one second (at a rate of 2 ms per century)" and "The [accumulated] difference between UTC and UT would reach 0.5 hours after the year 2600 and 6.5 hours around 4600" which I expect will be sufficient to take us through to the time where we will no longer need co-ordinated time or an IERS.
[0] https://en.wikipedia.org/wiki/Coordinated_Universal_Time
Time of day and calendaring and discussed together because they allow you to ask things like "what was the date and time on Mars prime meridian on Feb 2 2023 6:00 UTC" and get a recognizable date and time back. It's essentially a timezone, albeit a very strange one with a variable offset.
> modifying the core idea of the 24 hour day to be a "slight tweak"?
Ok, maybe an exaggerated hand-wave on my part. It's a slight software tweak on my desk clock. I was contrasting with the alternative of modifying a fundamental SI unit and more or less rebuilding from scratch all hardware sent on Mars. The fuckups alone resulting from confusing Earth seconds with Mars seconds.