Why do Doodle's parents name him William Armstrong?

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.

The story doesn't give a specific "this is why" reason for why Doodle's parents name him William Armstrong.  There is a big hint at the reason from Brother; however, the story is told from Brother's perspective, so the reason might be Brother's interpretation of Doodle's legal name.  
To begin with, Doodle's parents did not expect him to live very long.  When Doodle defied the odds and lived to be three months old, his parents decided that they had better give him a proper name.  They name him William Armstrong.  It's a good, solid sounding name, and that is what Brother comments on.  He says that William Armstrong is not a name that fits Doodle.  The name is only a good name because it will look good on a tombstone.  That's really depressing to think that Doodle's parents picked William Armstrong because it would appear strong and wonderful on Doodle's grave.  

Daddy had Mr. Heath, the carpenter, build a little mahogany coffin for him. But he didn't die, and when he was three months old, Mama and Daddy decided they might as well name him. They named him William Armstrong, which is like tying a big tail on a small kite. Such a name sounds good only on a tombstone.