Why does Beetle take on the name Alyce?

Alyce goes through some dramatic changes throughout the story. She is definitely a dynamic character, and her names are as dynamic as she is. What's interesting about her names is that Alyce never really chooses her new names. Other people call her a name, and she either adopts the name because she likes it, or she takes the name out of necessity.
When the reader is first introduced to Alyce, she is called Brat. When Jane finds her in a dung pile, Jane decides to call her "Beetle." That name stays with her for a large portion of the story. It's not until after Jane breaks her ankle that Beetle once again changes names. Jane cannot travel, so she sends Beetle instead to go buy supplies. While at the Saint Swithin's Day Fair, somebody mistakes Beetle for somebody else. He calls her Alyce. Beetle likes the name and takes it as her own. The name change is symbolic of her growing confidence. Alyce no longer feels like the weak girl found in a dung heap. She is gaining confidence in her skills, education, and looks. She realizes that "Beetle" is not a name that fits with how she feels. "Alyce" is a name that fits with who she feels she is becoming.

What a day! She had been winked at, complimented, given a gift, and now mistaken for the mysterious Alyce who could read. Did she then look like someone who could read? She leaned over and watched her face in the water again. "This face," she said, "could belong to someone who can read. And has curls. And could have a lover before nightfall."
"Alyce," she breathed. Alyce sounded clean and friendly and smart. You could love someone named Alyce. She looked back at the face in the water. "This then is me, Alyce." It was right.