In my head I keep a concept of "physical day" (real calendar days, followed by other, real calendar days) and "logical day", which is the day as I am currently experiencing or referring to it. If, after a long Monday, you're up past midnight (i.e, it is now Tuesday), then the "phyiscal" day is "Tuesday" and the logical day is "Monday". The logical day progresses either when you go to sleep (at which point one ends, and another begins when you wake), or at dawn.¹
Person to person speech is almost always in logical days; "tomorrow" would not be a minute past midnight in this system. This at least makes some things make sense.
¹There _still_ tons of issues with this, such as people who work at night and sleep during the day, people can be on different logical days, some places don't have a dawn for several months…
