New Year’s Eve and New Year’s Day always start with capital letters and always take an apostrophe. When you’re wishing someone “Happy New Year,” most sources say that New Year should be capitalized, too.
But dictionaries give conflicting advice on whether to capitalize the singular New Year. “Webster’s New World College Dictionary” lower-cases it. So technically, you could write “Happy new year.” But “Merriam-Webster’s” and “American Heritage” dictionaries both capitalize it: New Year.
If you’re talking in generic terms, you can use the plain-old noun “year” and modify it with the plain-old adjective “new” to get lowercase “new year.” This is especially common with “the”: “We will see many changes in the new year.”
The third Monday in January is Martin Luther King Jr. Day, which the “Associated Press Stylebook” and the “Chicago Manual of Style” list without a “Rev.” without a “Dr.” and without any commas setting off “Jr.”
Valentine’s Day always has an apostrophe and is always capitalized. Look this name up in “Webster’s New World” and you’ll see the definition is “Saint Valentine’s Day,” but look it up in “Merriam-Webster’s” and you’ll see “St. Valentine’s Day.” You can use any of these to refer to the holiday on which you give a valentine to your valentine. That’s because the noun forms that mean your sweetheart or a greeting card are both lowercase.
If only Presidents Day were as easy. The dictionaries say this holiday, celebrated the third Monday in February, is plural possessive: Presidents’ Day. But AP says it’s the apostrophe-less Presidents Day, in which the first word is functioning as an adjective and therefore is not possessive.