The narrator recognizes the irony in the name William Armstrong as soon as it is given to Doodle. He says that William Armstrong is not a name for a weak, disabled boy, as even just the phrase "Armstrong" implies the kind of strength Doodle does not have. He even goes so far as to say that this particular name sounds good only on a tombstone.
Doodle's survival itself is an ironic situation, since everyone expected him to die. They even had a casket built for him, making it even more ironic when he eventually survives and proves to be sane and cognizant. It is also ironic that his survival creates the real conflict in the story, since one would expect this to be a happy twist of fate; now the narrator must learn to reconcile his previous conceptions of a little brother with who Doodle really is.
This story has a sense of dramatic irony, created by its format as a retrospective. The present narrator knows exactly what is going to happen, and as more elements of foreshadowing are included, the readers come to realize early on, too, that something bad will happen to Doodle that removes him from the narrator's life. But the past form of the narrator has no idea, and he pays no attention to the warning signs, such as the death of the scarlet ibis. He continues to force Doodle to do things he cannot, and eventually it comes back to haunt him.
The Scarlet Ibis Questions and Answers
The Question and Answer section for The Scarlet Ibis is a great
resource to ask questions, find answers, and discuss the novel.