diff --git a/python/python/lancedb/functions.py b/python/python/lancedb/functions.py
index 2ab658293..c22bf927a 100644
--- a/python/python/lancedb/functions.py
+++ b/python/python/lancedb/functions.py
@@ -674,7 +674,7 @@ class RefreshColumnResult(_RemoteValue):
         return self.published_version
 
 
-_FUNCTION_NAME = re.compile(r"^[A-Za-z_][A-Za-z0-9_.-]*$")
+_FUNCTION_NAME = re.compile(r"^[A-Za-z_][A-Za-z0-9_]*$")
 
 _FUNCTION_BLOB_V2_TYPE = "blob_v2"
 _ARROW_EXTENSION_NAME_KEY = "ARROW:extension:name"
@@ -2106,6 +2106,8 @@ def udf(
         The synchronous callable, or the class whose instances are called.
     name : str, optional
         The remote Function name. Defaults to the callable name.
+        Must start with an ASCII letter or underscore and contain only ASCII
+        letters, digits, and underscores.
     input_schema : pyarrow.Schema, optional
         Explicit input fields in the exact order of the callable parameters.
         Must be provided together with ``output_schema``.
diff --git a/python/python/tests/test_first_class_function_slice2.py b/python/python/tests/test_first_class_function_slice2.py
index 61e511345..392becf8c 100644
--- a/python/python/tests/test_first_class_function_slice2.py
+++ b/python/python/tests/test_first_class_function_slice2.py
@@ -89,6 +89,27 @@ def test_scalar_udf_matches_shared_registration_golden_and_remains_callable():
     }
 
 
+@pytest.mark.parametrize(
+    "name", ["examples.image_info", "image-info", "image_info.", "image_info-"]
+)
+def test_udf_rejects_function_names_with_periods_or_hyphens(name):
+    with pytest.raises(ValueError, match="invalid Function name"):
+
+        @udf(name=name)
+        def image_info(value: int) -> int:
+            return value
+
+
+@pytest.mark.parametrize("name", ["image_info", "ImageInfo123", "_image_info", "f"])
+def test_udf_accepts_function_names_with_letters_digits_and_underscores(name):
+    @udf(name=name)
+    def image_info(value: int) -> int:
+        return value
+
+    assert image_info.registration_request.name == name
+    assert image_info(1) == 1
+
+
 def test_secret_bound_udf_matches_its_shared_registration_golden():
     assert analyze_caption("  hello  ") == "hello"
     bound = analyze_caption.bind_secrets(