diff --git a/python/cudf_polars/cudf_polars/containers/column.py b/python/cudf_polars/cudf_polars/containers/column.py
index a139927acab..49034b5f5c8 100644
--- a/python/cudf_polars/cudf_polars/containers/column.py
+++ b/python/cudf_polars/cudf_polars/containers/column.py
@@ -32,12 +32,23 @@ def __init__(self, column: plc.Column, name: str):
         self.order = plc.types.Order.ASCENDING
         self.null_order = plc.types.NullOrder.BEFORE
 
-    def rename(self, name: str) -> Column:
-        """Return a new column sharing data with a new name."""
-        return type(self)(self.obj, name).sorted_like(self)
-
     def sorted_like(self, like: Column, /) -> Self:
-        """Copy sortedness properties from a column onto self."""
+        """
+        Copy sortedness properties from a column onto self.
+
+        Parameters
+        ----------
+        like
+            The column to copy sortedness metadata from.
+
+        Returns
+        -------
+        Self with metadata set.
+
+        See Also
+        --------
+        set_sorted
+        """
         return self.set_sorted(
             is_sorted=like.is_sorted, order=like.order, null_order=like.null_order
         )
@@ -70,9 +81,22 @@ def set_sorted(
         self.null_order = null_order
         return self
 
-    def copy(self) -> Self:
-        """Return a shallow copy of the column."""
-        return type(self)(self.obj, self.name).sorted_like(self)
+    def copy(self, *, new_name: str | None = None) -> Self:
+        """
+        Return a shallow copy of the column.
+
+        Parameters
+        ----------
+        new_name
+            Optional new name for the copied column.
+
+        Returns
+        -------
+        New column sharing data with self.
+        """
+        return type(self)(
+            self.obj, self.name if new_name is None else new_name
+        ).sorted_like(self)
 
     def mask_nans(self) -> Self:
         """Return a copy of self with nans masked out."""
diff --git a/python/cudf_polars/cudf_polars/containers/dataframe.py b/python/cudf_polars/cudf_polars/containers/dataframe.py
index 0762724d555..2ed4298e993 100644
--- a/python/cudf_polars/cudf_polars/containers/dataframe.py
+++ b/python/cudf_polars/cudf_polars/containers/dataframe.py
@@ -139,7 +139,7 @@ def replace_columns(self, *columns: Column) -> Self:
     def rename_columns(self, mapping: Mapping[str, str]) -> Self:
         """Rename some columns."""
         return type(self)(
-            [c.rename(mapping.get(c.name, c.name)) for c in self.columns], self.scalars
+            [c.copy(new_name=mapping.get(c.name)) for c in self.columns], self.scalars
         )
 
     def select_columns(self, names: Set[str]) -> list[Column]: