I've tried having a unique calendar for my game world during decades of DMing, and although the players tried to use it, it's mostly a hastle and a waste of time and it doesn't reach the intended result of immersion.
So now, like @
Remathilis, I gave up a number of years ago. And honestly, I'm all the better for it. Using the usual Julian calendar feels like unloading a pack-sack full of rocks (or other useless load you might think about).
@
Kikuras: to me, accepting an invented calendar is not about playersmanship. It's about where do you wish that your players (and yourself) put their attention and energy during the game sessions? By using a unique calendar, it requires some degree of energy and time. For what? I've never found it really gave off a true return for the investment in the form of in-game immersion. On the contrary, whenever reference to calendar elements is required, it stops the role-playing to get everyone to the same page. One problem being that reference to the day of the week or the name of the month is not common enough for anyone to ever learn them by heart. Heck, players need to learn city and kingdom names, NPC names by the score, they need to learn the history of the world, the names of important artifacts, gods, foes, ... and then, add 7 weekday names and 12 month names?
DM- We shall meet on the first Bearday of the month of Ungust.
Player- Wait, what did he say?
DM- First Bearday of the month of Ungust.
Player- Hold on, let me take out the calendar... Just a sec, it's just here in my papers... Okay, got it. So, month of... Redmoon... Wolfpelt... Marust, that it?
DM- No, Ungust.
Player- Marust... Ungust, got it. What was the day again?
DM- Bearday.
Player- OKay, that's Tuesday, got it. (To the other players: ) that would be the first Tuesday of the fourth month. We're now in the month of Wolfpelt, so we're meeting in two months. So I reply (back to the DM, now in character) "Alright, Count, we will meet on the first Bearday of Ungust".
Note that the eventual reference of "Bearday is Tuesday" or "Bearday is the sixth day of the week", is pretty much unavoidable, because again players do not know the names of the weekdays by heart, so they need some reference (such as real day weekday names or weekday numbers, e.g. sixth day of the week) that can make them understand what they're talking about when they discuss time references amongst themselves. So, what is supposed to increase immersion, actually forces meta-conversations to occur.
I think that using invented calendars is popular at least in part because of books where authors do this. But, books are different: as a reader, you don't need to refer to the calendar, nor to count how many days are left before the meeting with the Count. You just read the book, period. The author does all the work for you. Not so in a D&D game.
As a side note, I likewise do not use very complex names for my locales, be them towns, cities, taverns, etc... I use names that are easily remembered, except in rare circumstances where I wish to truly convey a foreign connotation by using a weird-sounding name. For example, I'll have the city of Blacklake, or the small village of Hightower. Names like the city of "Kalikur'azastarhhhh'Ber'manek in the province of Kor'thura, which is right next to the provinces of Rek'thura and Barekin'thura" (DM has fun imagining some kind of similar-sounding names) are reallly fun to write down on a piece of paper, but when you have two dozen of those, your players only remember, like, very few, if you're lucky.
Anyway, whatever floats your boat is fine really. If using invented time references increases immersion and the quality of role-playing, or otherwise allows you to improve your gaming experience, go ahead! I'm just sharing my experience with you from the perspective of my gaming groups: it plays better with the Julian calendar.
