unbirthday
A day that is not one's birthday but is celebrated as though it were.
"They gave it me," Humpty Dumpty continued thoughtfully, as he crossed one knee over the other and clasped his hands round it, "they gave it me⸺for an un-birthday present." / "I beg your pardon?" Alice said with a puzzled air." / "I'm not offended," said Humpty Dumpty. / "I mean, what is an un-birthday present?" / "A present given when it isn't your birthday, of course."
Where it comes from
From un- + birthday, coined by English writer Lewis Carroll (1832–1898) in Through the Looking-Glass (1871).
Adapted from the Wiktionary entry unbirthday (CC BY-SA 4.0).