diff --git a/moto/organizations/exceptions.py b/moto/organizations/exceptions.py
index 01b98da7e..b40908862 100644
--- a/moto/organizations/exceptions.py
+++ b/moto/organizations/exceptions.py
@@ -10,3 +10,13 @@ class InvalidInputException(JsonRESTError):
             "InvalidInputException",
             "You provided a value that does not match the required pattern.",
         )
+
+
+class DuplicateOrganizationalUnitException(JsonRESTError):
+    code = 400
+
+    def __init__(self):
+        super(DuplicateOrganizationalUnitException, self).__init__(
+            "DuplicateOrganizationalUnitException",
+            "An OU with the same name already exists.",
+        )
diff --git a/moto/organizations/models.py b/moto/organizations/models.py
index 42e4dd00a..0db069f9a 100644
--- a/moto/organizations/models.py
+++ b/moto/organizations/models.py
@@ -8,7 +8,10 @@ from moto.core import BaseBackend, BaseModel
 from moto.core.exceptions import RESTError
 from moto.core.utils import unix_time
 from moto.organizations import utils
-from moto.organizations.exceptions import InvalidInputException
+from moto.organizations.exceptions import (
+    InvalidInputException,
+    DuplicateOrganizationalUnitException,
+)
 
 
 class FakeOrganization(BaseModel):
@@ -222,6 +225,14 @@ 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):
+        for ou in self.ou:
+            if ou.name == kwargs["Name"]:
+                raise DuplicateOrganizationalUnitException
+        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..876e83712 100644
--- a/tests/test_organizations/test_organizations_boto3.py
+++ b/tests/test_organizations/test_organizations_boto3.py
@@ -713,3 +713,41 @@ 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)
+
+
+@mock_organizations
+def test_update_organizational_unit_duplicate_error():
+    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)
+    with assert_raises(ClientError) as e:
+        client.update_organizational_unit(
+            OrganizationalUnitId=response["OrganizationalUnit"]["Id"], Name=ou_name
+        )
+    exc = e.exception
+    exc.operation_name.should.equal("UpdateOrganizationalUnit")
+    exc.response["Error"]["Code"].should.contain("DuplicateOrganizationalUnitException")
+    exc.response["Error"]["Message"].should.equal(
+        "An OU with the same name already exists."
+    )