It depends. On the one hand it's little annoying when author changes names just for the sake of a cosmetic change. So we basically still got an 12 month year 7 day week but Friday now names Furryday etc. But I do like figuring out a structure of a world if it makes deeper sense so I like well-worked worlds like Tolkien's or Le Guin's.

So you can don't make any change at all (I don't think that most people pays a lot of attention to calendars) or change it quite profoundly. I don't know a setting of your writing so it's just a bunch of PO ideas: you can invent something like Ancient Egypt system - they used to have 3 calendars Sun, Moon and Sirius with a "year" of different length. Or you could connect calendar to "meaning of time" like in Tzolken where any day of a cycle represent a specific stage of any process from planing task to thinking about results you accomplished. This may give you heroes an extra motivation for performing specific tasks on specific days etc