The text never really reveals why Doodle's parents name him William Armstrong. However, we can explore some possible reasons for Doodle's name.
First, the name is larger than life. It's one that gives an impression of robust health. When Doodle was born, his parents almost gave up on him. He was emaciated, and his head seemed larger than the rest of his body. Doodle's father even commissioned the carpenter to build a coffin for his newborn son; he had very little faith that his son would survive beyond his first moments of life.
When Doodle lived longer than three months, however, his parents proceeded to name him William Armstrong. First, the name highlights the fact that Doodle has beat the odds. So, his parents want his name to match his new status as a survivor. Second, such a robust name may have also given the parents hope that Doodle will continue to outlive his predicted life span.
The text does acknowledge, however, that Doodle's parents have few illusions about his name. "William Armstrong" is a superficial symbol of strength and tenacity, an effort to transcend the sad realities of Doodle's life. When Doodle begins moving around, the narrator decides to rename his little brother. He imagines that Doodle is a more appropriate name for a boy who just wants to be normal.