What is the correct way to refer to the end-of-year holiday which includes January's initial days? Like in Australia offices are usually closed between 25 December (Christmas day) to 1 January. Yes, I know officially only one day of the new year is a public holiday but still, many people take more days after it off (like five or six days of January), so I feel "Christmas holidays" or "End of year holidays" are not accurate.
Generally "Christmas holidays" is sufficient.
The school will have Christmas holidays from December 17th to January 3rd. The Easter holidays start on the first of April.
If you have a pedantic and legalist mindset then "Christmas and New Year's holidays", but it doesn't really need a special "name".