Most anime characters have birthdays that are canonically assigned by their creators. In some cases, that birthday will actually come up in the show itself, but most of the time, it's part of the supplementary information that can be found in guidebooks, official websites, and series' Wikia pages. While character birthdays don't usually make a huge difference in terms of story or character development, it's still a fun bit of trivia.
Even more fun is seeing which characters - some from wildly different series - have the same birthdays. There are only 365 days in the year, and there are thousands of characters, so it stands to reason that there are plenty of anime characters with the same birthday. Umetarou Nozaki from Monthly Girls' Nozaki-kun and Shinji Ikari from Neon Genesis Evangelion have little in common besides being teenage boys, and both have even less in common with Shinobu Sensui from Yu Yu Hakusho - but they were all born on June 6th.
Merry Christmas! This holiday - which in Japan is celebrated with fried chicken - is also the birthday of Death Note's Misa Amane, Assassination Classroom's Karma Akabane, and Yuri!!! on ICE's Victor Nikiforov. They're all pretty busy - Misa with helping Light kill criminals, Karma with trying to assassinate his teacher, and Victor with being famous - so it's unlikely that they'll get time to celebrate. Maybe they can at least eat some chicken?
How would LLENN from Sword Art Online Alternative: Gun Gale Online, Bakugo from My Hero Academia, and Catherine from Black Clover spend their birthday? Because their birthday falls on 4/20, aka weed's birthday, the answer is that they'd all be toking up. Maybe LLENN is only doing a simulation using a premium item from Gun Gale Online, and maybe Catherine's grass is actually magic, but there's not really any other way to spend this particular day.
Don't let Luffy from One Piece and Hijikata from Gintama have a birthday party together, because it will invariably end with Luffy breaking some kind of law and Hijikata arresting him. Even if Luffy doesn't do anything illegal, Hijikata might arrest him anyway because Luffy ate his way through Hijikata's stash of mayonnaise. Meanwhile, Gon Freecss is off having a nice birthday with other children - some of whom are definitely murderers, but hey, don't judge.
If Momo Yaoyorozu of My Hero Academia, Megumi Kato of Saekano: How To Raise A Boring Girlfriend and Takao Kawafuji of Barakamon got together to celebrate their September birthday, it would likely devolve into a brainstorming session about what kinds of things Momo can create with her quirk. After all, both Megumi and Kawafuji are in the business of prompting creative minds to get moving.
Afterward, Kawafuji would probably leave to have a cigarette and go harass his client Handa, and the two girls could go to the mall - something Megumi loves, and Momo is fascinated by.