* As a tree species: "Birch" is a common noun referring to a type of tree.
* As a person's name: "Birch" can be a proper noun, used as a given name or a surname.
Here are some examples:
Common noun: "The birch tree is known for its white bark."
Proper noun: "My friend Birch is a great artist."
So, whether "Birch" is a proper noun or not depends on the context.