diff --git a/python-package/lightgbm/basic.py b/python-package/lightgbm/basic.py
index 5e609bca45f9..05a4eb4c69c3 100644
--- a/python-package/lightgbm/basic.py
+++ b/python-package/lightgbm/basic.py
@@ -537,7 +537,7 @@ def _data_from_pandas(data, feature_name, categorical_feature, pandas_categorica
         if len(data.shape) != 2 or data.shape[0] < 1:
             raise ValueError('Input data must be 2 dimensional and non empty.')
         if feature_name == 'auto' or feature_name is None:
-            data = data.rename(columns=str)
+            data = data.rename(columns=str, copy=False)
         cat_cols = [col for col, dtype in zip(data.columns, data.dtypes) if isinstance(dtype, pd_CategoricalDtype)]
         cat_cols_not_ordered = [col for col in cat_cols if not data[col].cat.ordered]
         if pandas_categorical is None:  # train dataset
diff --git a/tests/python_package_test/test_basic.py b/tests/python_package_test/test_basic.py
index d290bcb7216c..e9b47a820757 100644
--- a/tests/python_package_test/test_basic.py
+++ b/tests/python_package_test/test_basic.py
@@ -644,22 +644,22 @@ def test_custom_objective_safety():
 
 
 @pytest.mark.parametrize('dtype', [np.float32, np.float64])
-def test_no_copy_when_single_float_dtype_dataframe(dtype):
+@pytest.mark.parametrize('feature_name', [['x1', 'x2'], 'auto'])
+def test_no_copy_when_single_float_dtype_dataframe(dtype, feature_name):
     pd = pytest.importorskip('pandas')
     X = np.random.rand(10, 2).astype(dtype)
     df = pd.DataFrame(X)
-    # feature names are required to not make a copy (rename makes a copy)
-    feature_name = ['x1', 'x2']
     built_data = lgb.basic._data_from_pandas(df, feature_name, None, None)[0]
     assert built_data.dtype == dtype
     assert np.shares_memory(X, built_data)
 
 
-def test_categorical_code_conversion_doesnt_modify_original_data():
+@pytest.mark.parametrize('feature_name', [['x1'], 'auto'])
+def test_categorical_code_conversion_doesnt_modify_original_data(feature_name):
     pd = pytest.importorskip('pandas')
     X = np.random.choice(['a', 'b'], 100).reshape(-1, 1)
     df = pd.DataFrame(X.copy(), columns=['x1'], dtype='category')
-    data = lgb.basic._data_from_pandas(df, ['x1'], None, None)[0]
+    data = lgb.basic._data_from_pandas(df, feature_name, None, None)[0]
     # check that the original data wasn't modified
     np.testing.assert_equal(df['x1'], X[:, 0])
     # check that the built data has the codes