The tree calls the boy "Boy" even after he grows up and becomes a teenager, a man, a middle-aged man, and an elderly man. This is the tree's way of indirectly saying, "Even if you're too old to spend time with me anymore, I'll always see you as but the little boy that used to swing from my branches and eat my apples and nap in my shade."
The tree calling the boy "Boy" is also a way of pointing out the metaphor for parenthood. We call our offspring our "children" even when they are fully grown. The boy is the Tree's "boy" in the same way a man would be his mother's "boy."