I am a proponent of a Martian timekeeping system where each day has 24 hours 39 minutes and 35.244 seconds and all the rest of time units have standard lengths. For example, at midnight your martian clock would show the time as 24:39:35 for a fraction of a second, then wound back to 00:00:00. The calendar then would track the Earth calendar as close as possible, with shortened months to accommodate for the longer days.

Basically, everything is roughly in sync with Earth and uses similar or identical units, except the time of day which is synced to the martian solar day, the only local time of relevance to the martians, for things like working light and circadian rhythm, solar panel irradiation etc. The "seasons" of Mars are of little relevance due to the very artificial conditions in which the martians will live, the weather outside is deadly all year long with slight variations in deadliness.

So the entire idea of keeping a martian calendar with funny month names doesn't really make sense, the only thing martians will care is the time of the next Earth transport and the dates on Earth so they can relate with their loved ones. As is the idea of having different lengths of seconds and hours, which will render almost all Earth equipment and measurements unusable, as opposed to a slight tweak in the software of their clocks to enable times past 23:59:59.