diff --git a/benchmarks/bench_rcv1_logreg_convergence.py b/benchmarks/bench_rcv1_logreg_convergence.py
index e8fce1c414abf..2254ab81f30a4 100644
--- a/benchmarks/bench_rcv1_logreg_convergence.py
+++ b/benchmarks/bench_rcv1_logreg_convergence.py
@@ -240,7 +240,7 @@ def get_max_squared_sum(X):
         SGDClassifier(
             alpha=1.0 / C / n_samples,
             penalty="l2",
-            loss="log",
+            loss="log_loss",
             fit_intercept=fit_intercept,
             verbose=0,
         ),
diff --git a/sklearn/linear_model/_logistic.py b/sklearn/linear_model/_logistic.py
index 6680d60cb4b1c..745fcbced7016 100644
--- a/sklearn/linear_model/_logistic.py
+++ b/sklearn/linear_model/_logistic.py
@@ -1013,7 +1013,7 @@ class LogisticRegression(LinearClassifierMixin, SparseCoefMixin, BaseEstimator):
     See Also
     --------
     SGDClassifier : Incrementally trained logistic regression (when given
-        the parameter ``loss="log"``).
+        the parameter ``loss="log_loss"``).
     LogisticRegressionCV : Logistic regression with built-in cross validation.
 
     Notes
diff --git a/sklearn/tests/test_multioutput.py b/sklearn/tests/test_multioutput.py
index ad95282fa6614..371c516f197c5 100644
--- a/sklearn/tests/test_multioutput.py
+++ b/sklearn/tests/test_multioutput.py
@@ -202,8 +202,8 @@ def test_hasattr_multi_output_predict_proba():
 
 # check predict_proba passes
 def test_multi_output_predict_proba():
-    sgd_linear_clf = SGDClassifier(random_state=1, max_iter=5, loss="log_loss")
-    param = {"loss": ("hinge", "log", "modified_huber")}
+    sgd_linear_clf = SGDClassifier(random_state=1, max_iter=5)
+    param = {"loss": ("hinge", "log_loss", "modified_huber")}
 
     # inner function for custom scoring
     def custom_scorer(estimator, X, y):
@@ -213,7 +213,11 @@ def custom_scorer(estimator, X, y):
             return 0.0
 
     grid_clf = GridSearchCV(
-        sgd_linear_clf, param_grid=param, scoring=custom_scorer, cv=3
+        sgd_linear_clf,
+        param_grid=param,
+        scoring=custom_scorer,
+        cv=3,
+        error_score="raise",
     )
     multi_target_linear = MultiOutputClassifier(grid_clf)
     multi_target_linear.fit(X, y)