Editing date/time

I would do a forum and google search prior to me asking this, however, I haven’t a clue where to begin my searches. I am building a roleplaying community that I want the date and times to be changed to increase immersion. To get a little more detailed, I am developing an Elder Scrolls roleplaying community whereas the dates and times are changed. Thankfully, these dates and times are the same as real-time, however, names are changed. Where do I go to change these names of months, days, etc.? And preferably, how would I do this without the use of a plugin?