My son certainly doesn’t know his name yet, but it’s how everyone addresses him. So it is definitely not an integral part of his identity, at least as he experiences it.
The name doesn’t have any meaning for me nor my wife. It is normal enough to be familiar, stands out enough to not disappear, is nice to abbreviate, sounds pleasing to our ears. But it also has nothing to do with him or his ancestry at all, except it’s ethnically congruous I guess.
So my son is not at all his name, probably for the only time in his life. It is a bit odd.