Why do Doodle's parents name him William Armstrong?
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.