There is a slight ambiguity here. Which measure of time are you referring to, here? The concept of years, months and weeks, or dividing a day into hours and minutes? Well, I will discuss both aspects briefly.
Concept Of Year, Months And Weeks
People here on earth have devised some remarkable ways of defining a year. Here are some prominent nominations and their variations for your world.
1- Lunar versus Solar calendars
This should be self evident. A lunar calendar is primarily based on defining a month (one complete cycle of a tidally locked moon). It then goes on to define a year as a group of x number of months. Contrary to this, a solar calendar primarily defines a year (one complete cycle of the planet around its parent star). It then goes on to define a month as a division of the year.
In your world, you can have solar and lunar years for different civilizations, and, depending on the number of moons the planet has, there could be several variations of the lunar year.
2- Different Month and Week definitions
Even for cultures which have the same number of days in a year (i.e. 365), there are several variations for defining the months. For example, the Julian calendar has 12 months with varying number of days, to a total of 365. Compare this to the Mayan calendar, which had 18 months of 20 days and another 5 days to complete 365.
Similarly, while most civilizations used a set of 7 days for the count of a week, the Mayan week consisted of only 5 days.
In your world, you could have an exotic method used by some civilizations, where they base their month on one moon and the weekday on another. The week-moon should be very predictive in its phases as week is the only solid, unchanged thing in the whole calendar.
I shall return to answer to add some discussion about division of a day into hours and minutes, if OP requires.