diff --git a/CHANGELOG.rst b/CHANGELOG.rst
index c47aded9..2c3b4e3d 100644
--- a/CHANGELOG.rst
+++ b/CHANGELOG.rst
@@ -4,6 +4,12 @@ Changelog
 unreleased
 **********
 
+Bug fixes:
+
+- ``schema2parameters``: Default parameter ``name`` to schema class name or
+  ``"body"`` if not specified (:issue:`829`).
+  Thanks :user:`rd3x` for reporting.
+
 Other changes:
 
 - Drop support for marshmallow 3, which is EOL.
diff --git a/src/apispec/ext/marshmallow/openapi.py b/src/apispec/ext/marshmallow/openapi.py
index 3663fce6..a8553195 100644
--- a/src/apispec/ext/marshmallow/openapi.py
+++ b/src/apispec/ext/marshmallow/openapi.py
@@ -139,8 +139,8 @@ def schema2parameters(
         self,
         schema,
         *,
-        location,
-        name: str = "body",
+        location: str,
+        name: str | None = None,
         required: bool = False,
         description: str | None = None,
     ):
@@ -157,6 +157,15 @@ def schema2parameters(
         location = __location_map__.get(location, location)
         # OAS 2 body parameter
         if location == "body":
+            if name is None:
+                if isinstance(schema, marshmallow.Schema):
+                    name = schema.__class__.__name__
+                elif isinstance(schema, type) and issubclass(
+                    schema, marshmallow.Schema
+                ):
+                    name = schema.__name__
+                else:
+                    name = "body"
             param = {
                 "in": location,
                 "required": required,
diff --git a/tests/test_ext_marshmallow_openapi.py b/tests/test_ext_marshmallow_openapi.py
index 9d832002..0f1cfd47 100644
--- a/tests/test_ext_marshmallow_openapi.py
+++ b/tests/test_ext_marshmallow_openapi.py
@@ -363,6 +363,28 @@ class UserSchema(Schema):
         assert param["schema"]["type"] == "array"
         assert param["schema"]["items"] == {"$ref": "#/definitions/User"}
 
+    # json/body is invalid for OpenAPI 3
+    @pytest.mark.parametrize("openapi", ("2.0",), indirect=True)
+    def test_schema_body_name_default(self, openapi):
+        class UserSchema(Schema):
+            name = fields.Str()
+
+        # Schema class defaults to class name
+        res = openapi.schema2parameters(UserSchema, location="body")
+        assert res[0]["name"] == "UserSchema"
+
+        # Schema instance defaults to class name
+        res = openapi.schema2parameters(UserSchema(), location="body")
+        assert res[0]["name"] == "UserSchema"
+
+        # Explicit name overrides default
+        res = openapi.schema2parameters(UserSchema, location="body", name="custom_name")
+        assert res[0]["name"] == "custom_name"
+
+        # Non-schema fallback defaults to "body"
+        res = openapi.schema2parameters("UserRef", location="body")
+        assert res[0]["name"] == "body"
+
     def test_schema_query(self, openapi):
         class UserSchema(Schema):
             name = fields.Str()