So, Anne of Green Gables might seem like an obvious title, since the book is about Anne and how she grows up. But then, the title isn't Anne Shirley, so the "of Green Gables" part is key. The title is about belonging, something Anne craved so desperately before she arrived at Green Gables. On one of her first days in her new home, Anne says to her reflection in the mirror,
"But it's a million times nicer to be Anne of Green Gables than Anne of nowhere in particular, isn't it?" (8.57)
Good point, Anne. She's just leveled up in terms of her social class and resources. More importantly, though, belonging somewhere makes her feel better about herself.
Later in the story, when Josephine Barry demands to know who she is, Anne responds, "I'm Anne of Green Gables." (19.80) Anne's home and community have shaped her, so much that they have become part of her identity.