fix(logger): preserve empty project names

py/src/braintrust/logger.py

@@ -1701,7 +1701,7 @@ def compute_metadata():
         state.login(org_name=org_name, api_key=api_key, app_url=app_url)
         if project_id is None:
             project_info = state.api_client().projects.post_project(
-                body={"name": project or GLOBAL_PROJECT, "org_name": state.org_name}
+                body={"name": project if project is not None else GLOBAL_PROJECT, "org_name": state.org_name}
             )
         else:
             project_info = state.api_client().projects.get_project_id(project_id)

py/src/braintrust/test_logger.py

@@ -141,6 +141,18 @@ def test_init_validation(self):
 
         assert str(cm.exception) == f"duplicate tag: {tag}"
 
+    def test_init_preserves_empty_project_name(self):
+        api_client = self._mock_api_client()
+        api_client.projects.post_project.return_value = {"id": "empty-project-id", "name": ""}
+
+        simulate_login()
+        with patch.object(logger._state, "api_client", return_value=api_client):
+            exp = braintrust.init(project="")
+            metadata = exp._lazy_metadata.get()
+
+        api_client.projects.post_project.assert_called_once_with(body={"name": "", "org_name": logger._state.org_name})
+        assert metadata.project.name == ""
+
     def test_init_with_repo_info_does_not_raise(self):
         """Test that passing repo_info to init() doesn't cause an UnboundLocalError.