Being dedicated to a business for a decade is really impressive too, especially in this age of job swapping. What do you think would be appropriate for a 10 year work anniversary gift?
Mine is a map of London postal code areas from 1912 (original, not a copy of course).
Received a gift for Christmas (which was a gift card, then a hamper) and when I quit on good terms (which was a watch).
Never received or heard of anyone receiving a birthday gift or anniversary (of what?) gift from work. Maybe if someone has been there 50 years, or something there might be something special.
To be honest if a boss-like individual purchased a personal gift for someone's birthday I don't find that odd. If the company does it, that is a little odd. Even if technically both gifts come from the same pool of money in some cases.
In a few startups I've worked at or heard about, you'd receive gifts on your yearly anniversary of your start date plus usually there'd be a cake and/or card for birthdays.
Can you explain why you'd feel odd if a company bought the birthday gift rather than the boss buying it?
Honestly I cannot.
It is just not the "done thing." People buy people presents on their birthday because they care. Companies give out Christmas bonus as almost part of your pay (almost), a company cannot "care" so giving you a birthday gift (which will likely be automated by a HR e-mail anyway) just seems awkward, like: "here is your autonomously generated birthday present."
Anniversaries at one company were commemorated by 1 year stickers that most people put on their name plate. Five and on were supposed to have more lavish rewards, such as a month-long sabbatical and so on.