A lot of science fiction writers try to address the problem of time when humanity becomes a space-faring race. Star Trek has the idea of a “Stardate” and instructed the script writers to just fucking make it up,
For example, 1313.5 is twelve o’clock noon of one day and 1314.5 would be noon of the next day. Each percentage point (sic) is roughly equivalent to one-tenth of one day. The progression of stardates in your script should remain constant but don’t worry about whether or not there is a progression from other scripts. Stardates are a mathematical formula which varies depending on location in the galaxy, velocity of travel, and other factors, can vary widely from episode to episode."
Meanwhile, Asimov in the Robots / Foundation universe, everyone still uses the idea of a 365-day / 24-hour day “year”, even if no one remembers Earth (except a R. Daneel Olivaw and a few others).
And Kim Stanley Robinson in his Mars trilogy does what OP notes – Martian years are longer, and the societies diverge pretty rapidly, within a generation, for a whole host of reasons.