We use have for planned or regular days off: We have Christmas Eve off/I have Mondays off. You could also say, Sunday and Monday are my days off, if these are your regular days of rest. People who work Monday through Friday generally only talk about days off which are unusual (not Saturday and Sunday).
We usually use take for days that we choose, outside of the normal timetable: I'm taking tomorrow off.
Some companies give their employees special days off, so people can make longer weekends from national holidays. Some companies also give people their birthdays off.
Please note: A day off is different from a day when you're ill. We call this a sick day, and you can see more vocabulary for this here.