diff --git a/moto/secretsmanager/models.py b/moto/secretsmanager/models.py
index e6cefd5a9..0fde0faaf 100644
--- a/moto/secretsmanager/models.py
+++ b/moto/secretsmanager/models.py
@@ -16,7 +16,7 @@ from .exceptions import (
     InvalidRequestException,
     ClientError,
 )
-from .utils import random_password, secret_arn, get_secret_name_from_arn
+from .utils import random_password, secret_arn, get_secret_name_from_partial_arn
 from .list_secrets.filters import (
     filter_all,
     tag_key,
@@ -176,25 +176,40 @@ class FakeSecret:
 
 
 class SecretsStore(dict):
+    # Parameters to this dictionary can be three possible values:
+    # names, full ARNs, and partial ARNs
+    # Every retrieval method should check which type of input it receives
+
     def __setitem__(self, key, value):
-        new_key = get_secret_name_from_arn(key)
-        super().__setitem__(new_key, value)
+        super().__setitem__(key, value)
 
     def __getitem__(self, key):
-        new_key = get_secret_name_from_arn(key)
-        return super().__getitem__(new_key)
+        for secret in dict.values(self):
+            if secret.arn == key or secret.name == key:
+                return secret
+        name = get_secret_name_from_partial_arn(key)
+        return super().__getitem__(name)
 
     def __contains__(self, key):
-        new_key = get_secret_name_from_arn(key)
-        return dict.__contains__(self, new_key)
+        for secret in dict.values(self):
+            if secret.arn == key or secret.name == key:
+                return True
+        name = get_secret_name_from_partial_arn(key)
+        return dict.__contains__(self, name)
 
     def get(self, key, *args, **kwargs):
-        new_key = get_secret_name_from_arn(key)
-        return super().get(new_key, *args, **kwargs)
+        for secret in dict.values(self):
+            if secret.arn == key or secret.name == key:
+                return secret
+        name = get_secret_name_from_partial_arn(key)
+        return super().get(name, *args, **kwargs)
 
     def pop(self, key, *args, **kwargs):
-        new_key = get_secret_name_from_arn(key)
-        return super().pop(new_key, *args, **kwargs)
+        for secret in dict.values(self):
+            if secret.arn == key or secret.name == key:
+                key = secret.name
+        name = get_secret_name_from_partial_arn(key)
+        return super().pop(name, *args, **kwargs)
 
 
 class SecretsManagerBackend(BaseBackend):
diff --git a/moto/secretsmanager/utils.py b/moto/secretsmanager/utils.py
index faf767a40..215237110 100644
--- a/moto/secretsmanager/utils.py
+++ b/moto/secretsmanager/utils.py
@@ -68,17 +68,20 @@ def secret_arn(account_id, region, secret_id):
     )
 
 
-def get_secret_name_from_arn(secret_id):
-    # can fetch by both arn and by name
-    # but we are storing via name
-    # so we need to change the arn to name
-    # if it starts with arn then the secret id is arn
-    if secret_id.startswith("arn:aws:secretsmanager:"):
+def get_secret_name_from_partial_arn(partial_arn: str) -> str:
+    # We can retrieve a secret either using a full ARN, or using a partial ARN
+    # name:        testsecret
+    # full ARN:    arn:aws:secretsmanager:us-west-2:123456789012:secret:testsecret-xxxxxx
+    # partial ARN: arn:aws:secretsmanager:us-west-2:123456789012:secret:testsecret
+    #
+    # This method only deals with partial ARN's, and will return the name: testsecret
+    #
+    # If you were to pass in  full url, this method will return 'testsecret-xxxxxx' - which has no meaning on it's own
+    if partial_arn.startswith("arn:aws:secretsmanager:"):
         # split the arn by colon
         # then get the last value which is the name appended with a random string
-        # then remove the random string
-        secret_id = "-".join(secret_id.split(":")[-1].split("-")[:-1])
-    return secret_id
+        return partial_arn.split(":")[-1]
+    return partial_arn
 
 
 def _exclude_characters(password, exclude_characters):
diff --git a/tests/test_secretsmanager/test_secretsmanager.py b/tests/test_secretsmanager/test_secretsmanager.py
index ec42aed7c..6eee8b762 100644
--- a/tests/test_secretsmanager/test_secretsmanager.py
+++ b/tests/test_secretsmanager/test_secretsmanager.py
@@ -547,17 +547,26 @@ def test_describe_secret():
 
 
 @mock_secretsmanager
-def test_describe_secret_with_arn():
+@pytest.mark.parametrize("name", ["testsecret", "test-secret"])
+def test_describe_secret_with_arn(name):
     conn = boto3.client("secretsmanager", region_name="us-west-2")
-    results = conn.create_secret(Name="test-secret", SecretString="foosecret")
+    results = conn.create_secret(Name=name, SecretString="foosecret")
 
     secret_description = conn.describe_secret(SecretId=results["ARN"])
 
     assert secret_description  # Returned dict is not empty
-    secret_description["Name"].should.equal("test-secret")
+    secret_description["Name"].should.equal(name)
     secret_description["ARN"].should.equal(results["ARN"])
     conn.list_secrets()["SecretList"][0]["ARN"].should.equal(results["ARN"])
 
+    # We can also supply a partial ARN
+    partial_arn = f"arn:aws:secretsmanager:us-west-2:{ACCOUNT_ID}:secret:{name}"
+    resp = conn.get_secret_value(SecretId=partial_arn)
+    assert resp["Name"] == name
+
+    resp = conn.describe_secret(SecretId=partial_arn)
+    assert resp["Name"] == name
+
 
 @mock_secretsmanager
 def test_describe_secret_with_KmsKeyId():