If it's an uncommon proper name, and those things happen every single day, then the real-time captioners do not have that name in their dictionary. They either have to laboriously spell it letter by letter, and that can happen several times in the course of a sentence, or just put in frenetic strokes and hope it gets translated correctly, and that often doesn't work. By the next day, though, if that name is still in the news, the name is put in the dictionary, but you won't see that.
Delays—are you also referring to real-time captioning on live shows?