In the West, or at least the US, there's also the broad prohibition against picking your own nickname.
In the words of Frankie Boyle, the response to "Hey guys, you can call me T-dog!" is "Tony, we'll be calling you cuntychops from now on."
I think the closest most of us come is in internet communities, where we pick a handle - and then, as often as not, that identity is persistent, both to keep you findable and because it's /yours/ now.
I've had a lot of online names, bit I'm Nome here not because it's my name (though it is),
I actually baked kids picking their own names into the culture of the "fantasy" world in my comic. They don't have genders and people choose their adult names at age 12 (which was really my clever way of letting them have silly names like "Ampersand" đź¤).