diff --git a/README.md b/README.md
index 5cecc86..5f49933 100644
--- a/README.md
+++ b/README.md
@@ -20,7 +20,8 @@ poetry bundle venv .build/.venv --without dev
 package-python-function .build/.venv --output-dir .build/lambda
 ```
 
-The output will be a .zip file with the same name as your project from your pyproject.toml file.
+The output will be a .zip file with the same name as your project from your pyproject.toml file (with dashes replaced
+with underscores).
 
 ## Installation
 Use [pipx](https://github.com/pypa/pipx) to install:
@@ -40,7 +41,7 @@ One of the following must be specified:
 - `--output`: The full output path of the final zip file.
 
 - `--output-dir`: The output directory for the final zip file.  The name of the zip file will be based on the project's
-name in the pyproject.toml file.
+name in the pyproject.toml file (with dashes replaced with underscores).
 
 
 
diff --git a/package_python_function/packager.py b/package_python_function/packager.py
index a5b2feb..b3d1d7d 100644
--- a/package_python_function/packager.py
+++ b/package_python_function/packager.py
@@ -18,7 +18,7 @@ def __init__(self, venv_path: Path, project_path: Path, output_dir: Path, output
         self.venv_path = venv_path
 
         self.output_dir = output_file.parent if output_file else output_dir
-        self.output_file = output_file if output_file else output_dir / f'{self.project.name}.zip'
+        self.output_file = output_file if output_file else output_dir / f'{self.project.distribution_name}.zip'
 
         self._uncompressed_bytes = 0
 
diff --git a/package_python_function/python_project.py b/package_python_function/python_project.py
index 60021a3..f12b563 100644
--- a/package_python_function/python_project.py
+++ b/package_python_function/python_project.py
@@ -2,6 +2,7 @@
 from pathlib import Path
 from typing import Optional
 import tomllib
+import re
 
 
 class PythonProject:
@@ -16,6 +17,16 @@ def name(self) -> str:
             ('tool', 'poetry', 'name'),
         ))
 
+    """
+    Get the normalized name of the distribution, according to the Python Packaging Authority (PyPa) guidelines.
+    This is used to create the name of the zip file.
+    The name is normalized by replacing any non-alphanumeric characters with underscores.
+    https://peps.python.org/pep-0427/#escaping-and-unicode
+    """
+    @cached_property
+    def distribution_name(self) -> str:
+        return re.sub("[^\w\d.]+", "_", self.name, re.UNICODE)
+
     @cached_property
     def entrypoint_package_name(self) -> str:
         """
@@ -23,7 +34,7 @@ def entrypoint_package_name(self) -> str:
         code.
         """
         # TODO : Parse out the project's package dir(s) if defined.  Use the first one if there are multiple.
-        return self.name.replace('-', '_')
+        return self.distribution_name
 
     def find_value(self, paths: tuple[tuple[str]]) -> str:
         for path in paths:
diff --git a/scripts/poc/inner_package/other_package/other_package_module.py b/scripts/poc/inner_package/other_package/other_package_module.py
index 76ca296..0d7dbb7 100644
--- a/scripts/poc/inner_package/other_package/other_package_module.py
+++ b/scripts/poc/inner_package/other_package/other_package_module.py
@@ -1,2 +1,8 @@
+import logging
+
+logger = logging.getLogger(__name__)
+
+logger.info("Load")
+
 def other_package_module():
-    print("other_package_module")
\ No newline at end of file
+    logger.info("Hello from other_package_module")
\ No newline at end of file
diff --git a/scripts/poc/inner_package/zip_in_zip_test/__init__.py b/scripts/poc/inner_package/zip_in_zip_test/__init__.py
index 03aa4d9..1dfb4b2 100644
--- a/scripts/poc/inner_package/zip_in_zip_test/__init__.py
+++ b/scripts/poc/inner_package/zip_in_zip_test/__init__.py
@@ -1,6 +1,10 @@
 # This file represents the original module's __init__.py file that gets renamed when creating the innner ZIP.
 
-print("__init__ original")
+import logging
+
+logger = logging.getLogger(__name__ + "(__init__.py ORIGINAL)")
+
+logger.info("Hello, I am the original pacakge __init__.py")
 
 GLOBAL_VALUE_IN_INIT_ORIGINAL = "This global is defined in the original __init__.py"
 
diff --git a/scripts/poc/inner_package/zip_in_zip_test/main.py b/scripts/poc/inner_package/zip_in_zip_test/main.py
index 5192f03..3e6147f 100644
--- a/scripts/poc/inner_package/zip_in_zip_test/main.py
+++ b/scripts/poc/inner_package/zip_in_zip_test/main.py
@@ -1,10 +1,14 @@
-print("main.py: Load")
+import logging
+
+logger = logging.getLogger(__name__)
+
+logger.info("main.py: Load")
 
 from zip_in_zip_test import GLOBAL_VALUE_IN_INIT_ORIGINAL, other_module_function
 from other_package.other_package_module import other_package_module
 
 def main():
-    print("Hello from main!")
-    print(GLOBAL_VALUE_IN_INIT_ORIGINAL)
+    logger.info("Hello from main!")
+    logger.info(GLOBAL_VALUE_IN_INIT_ORIGINAL)
     other_module_function()
     other_package_module()
\ No newline at end of file
diff --git a/scripts/poc/inner_package/zip_in_zip_test/other_module.py b/scripts/poc/inner_package/zip_in_zip_test/other_module.py
index 51e1982..0244bee 100644
--- a/scripts/poc/inner_package/zip_in_zip_test/other_module.py
+++ b/scripts/poc/inner_package/zip_in_zip_test/other_module.py
@@ -1,2 +1,8 @@
+import logging
+
+logger = logging.getLogger(__name__)
+
+logger.info("Load")
+
 def other_module_function():
-    print("I'm in other_module_function")
\ No newline at end of file
+    logger.info("I'm in other_module_function")
\ No newline at end of file
diff --git a/scripts/poc/lambda-runner.py b/scripts/poc/lambda-runner.py
index 836991d..4c0dc8d 100644
--- a/scripts/poc/lambda-runner.py
+++ b/scripts/poc/lambda-runner.py
@@ -1,12 +1,15 @@
 # This is my best attempt at simulating what AWS Lambda does
 # Instead of messing with zipping and unzipping in this experiment, I just copy the files to the .test directory.
 
+import logging
 from pathlib import Path
 import shutil
 import sys
 
-print('[lambda-runner]')
-print('sys.path:', sys.path)
+logging.basicConfig(level=logging.INFO, stream=sys.stdout)
+logger = logging.getLogger("lambda-runner.py")
+
+logger.info('BEGIN')
 
 module_path = Path(__file__).parent
 TEST_DIR = module_path / ".test"
@@ -14,11 +17,19 @@
 TEST_PACKAGE_DIR = TEST_DIR / PACKAGE_NAME
 
 shutil.rmtree(TEST_DIR, ignore_errors=True)
+
+# Copy the stub `zip_in_zip_test` package to the .test directory. This simulates the outer ZIP extraction
+# that lambda will do.  This is the module that Lambda will import, and where we will do the inner ZIP extraction.
 shutil.copytree(str(module_path / PACKAGE_NAME), str(TEST_PACKAGE_DIR))
+
+# Copy the inner package to the .test directory. This simulates the inner ZIP file, but without actually dealing
+# with zip/unzip in this experiemen.
 shutil.copytree(str(module_path / "inner_package"), str(TEST_PACKAGE_DIR / ".inner_package"))
 
 sys.path.insert(0, str(TEST_DIR))
 
+logger.info('--- Importing entrypoint module ---')
 import importlib
 module = importlib.import_module('zip_in_zip_test.main')
+logger.info('--- Calling entryoint function ---')
 module.__dict__['main']()
diff --git a/scripts/poc/zip_in_zip_test/__init__.py b/scripts/poc/zip_in_zip_test/__init__.py
index 7f0186d..a326477 100644
--- a/scripts/poc/zip_in_zip_test/__init__.py
+++ b/scripts/poc/zip_in_zip_test/__init__.py
@@ -1,14 +1,20 @@
-# This works perfectly!
-
-print('zip_in_zip_test.__init__: BEGIN.  This is the loader.')
-print("module_path:", __file__)
-
+"""
+Demonstrate how we can swap out the content an entire package during the __init__.py load process of that package.
+"""
 from pathlib import Path
 import importlib
 import sys
+import logging
+
+logger = logging.getLogger(__name__ + "(__init__.py loader)")
+
+logger.info(f'BEGIN.  This is the loader.  {__file__}')
 
 module_path = Path(__file__).parent
 
+# This is where we would unzip the inner ZIP file.  For this experiment, we can skip actually doing that and pretend
+# that it was extracted to .inner_package/
+
 # This works if I insert at zero.
 # Why does the serverless-python-requirements insist on inserting at 1?
 # From https://docs.aws.amazon.com/lambda/latest/dg/python-package.html#python-package-searchpath:
@@ -17,6 +23,7 @@
 
 # This also works.  I am thinking this is the best way, because we need to unmount the original decompressed directory
 # since it contains the load __init__.py.
+previous_sys_path_root = sys.path[0]
 sys.path[0] = str(module_path / ".inner_package")
 
 
@@ -30,6 +37,7 @@
 # importlib.import_module(__name__)
 
 # This also works.  I think this is the best way.
+logger.info(f'Reloading {__name__} after switching {previous_sys_path_root} to {sys.path[0]}.')
 importlib.reload(sys.modules[__name__])
 
-print('zip_in_zip_test.__init__: END')
\ No newline at end of file
+logger.info('END')
\ No newline at end of file
diff --git a/tests/test_package_python_function.py b/tests/test_package_python_function.py
index 88bdc43..5d0ba3a 100644
--- a/tests/test_package_python_function.py
+++ b/tests/test_package_python_function.py
@@ -34,4 +34,4 @@ def test_package_python_function(tmp_path: Path) -> None:
     ]
     main()
 
-    assert (output_dir_path / 'project-1.zip').exists()
\ No newline at end of file
+    assert (output_dir_path / 'project_1.zip').exists()
\ No newline at end of file