diff --git a/moto/organizations/models.py b/moto/organizations/models.py
index 42e4dd00a..9be129fa7 100644
--- a/moto/organizations/models.py
+++ b/moto/organizations/models.py
@@ -222,6 +222,11 @@ class OrganizationsBackend(BaseBackend):
         self.attach_policy(PolicyId=utils.DEFAULT_POLICY_ID, TargetId=new_ou.id)
         return new_ou.describe()
 
+    def update_organizational_unit(self, **kwargs):
+        ou = self.get_organizational_unit_by_id(kwargs["OrganizationalUnitId"])
+        ou.name = kwargs["Name"]
+        return ou.describe()
+
     def get_organizational_unit_by_id(self, ou_id):
         ou = next((ou for ou in self.ou if ou.id == ou_id), None)
         if ou is None:
diff --git a/moto/organizations/responses.py b/moto/organizations/responses.py
index 7c42eb4ec..ba7dd4453 100644
--- a/moto/organizations/responses.py
+++ b/moto/organizations/responses.py
@@ -36,6 +36,11 @@ class OrganizationsResponse(BaseResponse):
             self.organizations_backend.create_organizational_unit(**self.request_params)
         )
 
+    def update_organizational_unit(self):
+        return json.dumps(
+            self.organizations_backend.update_organizational_unit(**self.request_params)
+        )
+
     def describe_organizational_unit(self):
         return json.dumps(
             self.organizations_backend.describe_organizational_unit(
diff --git a/tests/test_organizations/test_organizations_boto3.py b/tests/test_organizations/test_organizations_boto3.py
index dd79ae787..ab3ddf671 100644
--- a/tests/test_organizations/test_organizations_boto3.py
+++ b/tests/test_organizations/test_organizations_boto3.py
@@ -713,3 +713,20 @@ def test_untag_resource_errors():
     ex.response["Error"]["Message"].should.equal(
         "You provided a value that does not match the required pattern."
     )
+
+
+@mock_organizations
+def test_update_organizational_unit():
+    client = boto3.client("organizations", region_name="us-east-1")
+    org = client.create_organization(FeatureSet="ALL")["Organization"]
+    root_id = client.list_roots()["Roots"][0]["Id"]
+    ou_name = "ou01"
+    response = client.create_organizational_unit(ParentId=root_id, Name=ou_name)
+    validate_organizational_unit(org, response)
+    response["OrganizationalUnit"]["Name"].should.equal(ou_name)
+    new_ou_name = "ou02"
+    response = client.update_organizational_unit(
+        OrganizationalUnitId=response["OrganizationalUnit"]["Id"], Name=new_ou_name
+    )
+    validate_organizational_unit(org, response)
+    response["OrganizationalUnit"]["Name"].should.equal(new_ou_name)