diff --git a/moto/ssm/models.py b/moto/ssm/models.py
index 5c2a5cce7..775219ee1 100644
--- a/moto/ssm/models.py
+++ b/moto/ssm/models.py
@@ -1007,7 +1007,7 @@ class SimpleSystemManagerBackend(BaseBackend):
                     if (
                         "//" in value
                         or not value.startswith("/")
-                        or not re.match("^[a-zA-Z0-9_.-/]*$", value)
+                        or not re.match(r"^[a-zA-Z0-9_.\-/]*$", value)
                     ):
                         raise ValidationException(
                             'The parameter doesn\'t meet the parameter name requirements. The parameter name must begin with a forward slash "/". '
diff --git a/tests/test_ssm/test_ssm_boto3.py b/tests/test_ssm/test_ssm_boto3.py
index 73b80c893..b1dc63709 100644
--- a/tests/test_ssm/test_ssm_boto3.py
+++ b/tests/test_ssm/test_ssm_boto3.py
@@ -227,43 +227,46 @@ def test_get_parameters_by_path():
     )
 
 
+@pytest.mark.parametrize("name", ["test", "my-cool-parameter"])
 @mock_ssm
-def test_put_parameter():
+def test_put_parameter(name):
     client = boto3.client("ssm", region_name="us-east-1")
 
     response = client.put_parameter(
-        Name="test", Description="A test parameter", Value="value", Type="String"
+        Name=name, Description="A test parameter", Value="value", Type="String"
     )
 
     response["Version"].should.equal(1)
 
-    response = client.get_parameters(Names=["test"], WithDecryption=False)
+    response = client.get_parameters(Names=[name], WithDecryption=False)
 
     len(response["Parameters"]).should.equal(1)
-    response["Parameters"][0]["Name"].should.equal("test")
+    response["Parameters"][0]["Name"].should.equal(name)
     response["Parameters"][0]["Value"].should.equal("value")
     response["Parameters"][0]["Type"].should.equal("String")
     response["Parameters"][0]["Version"].should.equal(1)
     response["Parameters"][0]["LastModifiedDate"].should.be.a(datetime.datetime)
     response["Parameters"][0]["ARN"].should.equal(
-        "arn:aws:ssm:us-east-1:1234567890:parameter/test"
+        "arn:aws:ssm:us-east-1:1234567890:parameter/{}".format(name)
     )
     initial_modification_date = response["Parameters"][0]["LastModifiedDate"]
 
     try:
         client.put_parameter(
-            Name="test", Description="desc 2", Value="value 2", Type="String"
+            Name=name, Description="desc 2", Value="value 2", Type="String"
         )
         raise RuntimeError("Should fail")
     except botocore.exceptions.ClientError as err:
         err.operation_name.should.equal("PutParameter")
-        err.response["Error"]["Message"].should.equal("Parameter test already exists.")
+        err.response["Error"]["Message"].should.equal(
+            "Parameter {} already exists.".format(name)
+        )
 
-    response = client.get_parameters(Names=["test"], WithDecryption=False)
+    response = client.get_parameters(Names=[name], WithDecryption=False)
 
     # without overwrite nothing change
     len(response["Parameters"]).should.equal(1)
-    response["Parameters"][0]["Name"].should.equal("test")
+    response["Parameters"][0]["Name"].should.equal(name)
     response["Parameters"][0]["Value"].should.equal("value")
     response["Parameters"][0]["Type"].should.equal("String")
     response["Parameters"][0]["Version"].should.equal(1)
@@ -271,24 +274,20 @@ def test_put_parameter():
         initial_modification_date
     )
     response["Parameters"][0]["ARN"].should.equal(
-        "arn:aws:ssm:us-east-1:1234567890:parameter/test"
+        "arn:aws:ssm:us-east-1:1234567890:parameter/{}".format(name)
     )
 
     response = client.put_parameter(
-        Name="test",
-        Description="desc 3",
-        Value="value 3",
-        Type="String",
-        Overwrite=True,
+        Name=name, Description="desc 3", Value="value 3", Type="String", Overwrite=True,
     )
 
     response["Version"].should.equal(2)
 
-    response = client.get_parameters(Names=["test"], WithDecryption=False)
+    response = client.get_parameters(Names=[name], WithDecryption=False)
 
     # without overwrite nothing change
     len(response["Parameters"]).should.equal(1)
-    response["Parameters"][0]["Name"].should.equal("test")
+    response["Parameters"][0]["Name"].should.equal(name)
     response["Parameters"][0]["Value"].should.equal("value 3")
     response["Parameters"][0]["Type"].should.equal("String")
     response["Parameters"][0]["Version"].should.equal(2)
@@ -296,7 +295,7 @@ def test_put_parameter():
         initial_modification_date
     )
     response["Parameters"][0]["ARN"].should.equal(
-        "arn:aws:ssm:us-east-1:1234567890:parameter/test"
+        "arn:aws:ssm:us-east-1:1234567890:parameter/{}".format(name)
     )
 
 
@@ -1393,7 +1392,7 @@ def test_label_parameter_version_invalid_name():
 
     test_parameter_name = "test"
 
-    response = client.label_parameter_version.when.called_with(
+    client.label_parameter_version.when.called_with(
         Name=test_parameter_name, Labels=["test-label"]
     ).should.throw(
         ClientError,
@@ -1414,7 +1413,7 @@ def test_label_parameter_version_invalid_parameter_version():
         Type="String",
     )
 
-    response = client.label_parameter_version.when.called_with(
+    client.label_parameter_version.when.called_with(
         Name=test_parameter_name, Labels=["test-label"], ParameterVersion=5
     ).should.throw(
         ClientError,