the notion of a 'birthday', a time to celebrate a person, is a wonderful one. but a lot of aspects of how it's defined feel very detached from who the person is, and also the calendar we typically use for it is one that doesn't feel very significant to me. i think a system for a self-time that is built independent of calendars but also constructed by oneself or one's community is one that might be much more significant.
my suggestion: get together with some friends; have some paper and writing utensils, maybe a whiteboard for brainstorming. each of you take turns as the focus of the group, talking about what you're like and in what ways you're connected to your environment. after a bit, work with your friends to construct a poem, a structure of "when"s and "while"s and "after"s, which is a moment that seems to reflect your self. if you're feeling spicy, "when"s, "whither"s, "whence"s too. a moment in space, inseparable from you somehow.
truly, you are every moment you embody. but you can give a future self a name before they can know they exist. you can give them the understanding: someone took the time to think of you. someone knew you would be. before they, too, move onto the next moment something that shares your name will embody.