diff --git a/src/syrupy/serializers/raw_single.py b/src/syrupy/serializers/raw_single.py
index e4ef8c15..6c040a67 100644
--- a/src/syrupy/serializers/raw_single.py
+++ b/src/syrupy/serializers/raw_single.py
@@ -34,7 +34,12 @@ def discover_snapshots(self, filepath: str) -> "SnapshotFile":
         return snapshot_file
 
     def get_file_basename(self, index: int) -> str:
-        return self.__clean_filename(self.get_snapshot_name(index=index))
+        return self.get_snapshot_name(index=index)
+
+    def get_snapshot_name(self, index: int = 0) -> str:
+        return self.__clean_filename(
+            super(RawSingleSnapshotSerializer, self).get_snapshot_name(index=index)
+        )
 
     @property
     def snapshot_subdirectory_name(self) -> str:
diff --git a/tests/__snapshots__/test_amber_serializer.ambr b/tests/__snapshots__/test_amber_serializer.ambr
index ccb6700d..e1545f21 100644
--- a/tests/__snapshots__/test_amber_serializer.ambr
+++ b/tests/__snapshots__/test_amber_serializer.ambr
@@ -1,6 +1,15 @@
-# name: TestClass.test_name
+# name: TestClass.test_class_method_name
   'this is in a test class'
 ---
+# name: TestClass.test_class_method_parametrized[a]
+  'a'
+---
+# name: TestClass.test_class_method_parametrized[b]
+  'b'
+---
+# name: TestClass.test_class_method_parametrized[c]
+  'c'
+---
 # name: test_bool[False]
   False
 ---
diff --git a/tests/__snapshots__/test_raw_single_serializer/TestClass.test_class_method_name.raw b/tests/__snapshots__/test_raw_single_serializer/TestClass.test_class_method_name.raw
new file mode 100644
index 00000000..20661334
--- /dev/null
+++ b/tests/__snapshots__/test_raw_single_serializer/TestClass.test_class_method_name.raw
@@ -0,0 +1 @@
+this is in a test class
\ No newline at end of file
diff --git a/tests/__snapshots__/test_raw_single_serializer/TestClass.test_class_method_parametrizedx.raw b/tests/__snapshots__/test_raw_single_serializer/TestClass.test_class_method_parametrizedx.raw
new file mode 100644
index 00000000..c1b0730e
--- /dev/null
+++ b/tests/__snapshots__/test_raw_single_serializer/TestClass.test_class_method_parametrizedx.raw
@@ -0,0 +1 @@
+x
\ No newline at end of file
diff --git a/tests/__snapshots__/test_raw_single_serializer/TestClass.test_class_method_parametrizedy.raw b/tests/__snapshots__/test_raw_single_serializer/TestClass.test_class_method_parametrizedy.raw
new file mode 100644
index 00000000..e25f1814
--- /dev/null
+++ b/tests/__snapshots__/test_raw_single_serializer/TestClass.test_class_method_parametrizedy.raw
@@ -0,0 +1 @@
+y
\ No newline at end of file
diff --git a/tests/__snapshots__/test_raw_single_serializer/TestClass.test_class_method_parametrizedz.raw b/tests/__snapshots__/test_raw_single_serializer/TestClass.test_class_method_parametrizedz.raw
new file mode 100644
index 00000000..fa7af8bf
--- /dev/null
+++ b/tests/__snapshots__/test_raw_single_serializer/TestClass.test_class_method_parametrizedz.raw
@@ -0,0 +1 @@
+z
\ No newline at end of file
diff --git a/tests/test_amber_serializer.py b/tests/test_amber_serializer.py
index bb24cfa9..c7513fcc 100644
--- a/tests/test_amber_serializer.py
+++ b/tests/test_amber_serializer.py
@@ -96,5 +96,9 @@ def test_cycle(cyclic, snapshot):
 
 
 class TestClass:
-    def test_name(self, snapshot):
+    def test_class_method_name(self, snapshot):
         assert snapshot == "this is in a test class"
+
+    @pytest.mark.parametrize("actual", ["a", "b", "c"])
+    def test_class_method_parametrized(self, snapshot, actual):
+        assert snapshot == actual
diff --git a/tests/test_raw_single_serializer.py b/tests/test_raw_single_serializer.py
index c29fed8f..20141451 100644
--- a/tests/test_raw_single_serializer.py
+++ b/tests/test_raw_single_serializer.py
@@ -27,3 +27,12 @@ def test_does_not_write_non_binary(testdir, snapshot_raw: "SnapshotAssertion"):
     with pytest.raises(TypeError, match="Expected 'bytes', got 'str'"):
         snapshot_raw.serializer._write_snapshot_to_file(snapshot_file)
     assert not os.path.exists(snapshot_file.filepath)
+
+
+class TestClass:
+    def test_class_method_name(self, snapshot_raw):
+        assert snapshot_raw == b"this is in a test class"
+
+    @pytest.mark.parametrize("content", [b"x", b"y", b"z"])
+    def test_class_method_parametrized(self, snapshot_raw, content):
+        assert snapshot_raw == content