diff --git a/stacks/custom_domain.go b/stacks/custom_domain.go
index 3644e2d..cec119b 100644
--- a/stacks/custom_domain.go
+++ b/stacks/custom_domain.go
@@ -89,6 +89,7 @@ type CustomDomainStackParameters struct {
 	HostedZone       string
 	ClusterStackName string
 	PrimaryDomain    string
+	CertificateName  string
 	AltDomain1       string
 	AltDomain2       string
 	AltDomain3       string
@@ -141,6 +142,8 @@ func (p *CustomDomainStackParameters) SetInternalFields(sess *session.Session, n
 	}
 	p.HostedZone = strings.Split(*zone.Id, "/")[2]
 	ui.Spinner.Stop()
+	// `*` is not allowed in certificate names
+	p.CertificateName = strings.Replace(*name, "*", "wildcard", -1)
 	return nil
 }
 
@@ -182,10 +185,9 @@ func (*CustomDomainStack) AskQuestions(_ *session.Session) error {
 }
 
 func (*CustomDomainStack) StackName(name *string) *string {
-	stackName := fmt.Sprintf(
-		customDomainStackNameTmpl,
-		strings.ReplaceAll(strings.TrimSuffix(*name, "."), ".", "-"),
-	)
+	slug := strings.ReplaceAll(strings.TrimSuffix(*name, "."), ".", "-")
+	slug = strings.ReplaceAll(slug, "*", "wildcard")
+	stackName := fmt.Sprintf(customDomainStackNameTmpl, slug)
 	return &stackName
 }
 
@@ -193,9 +195,9 @@ func (*CustomDomainStack) StackType() string {
 	return "custom domain"
 }
 
-func (*CustomDomainStack) Tags(name *string) []*cloudformation.Tag {
+func (a *CustomDomainStack) Tags(name *string) []*cloudformation.Tag {
 	return []*cloudformation.Tag{
-		{Key: aws.String("apppack:customDomain"), Value: name},
+		{Key: aws.String("apppack:customDomain"), Value: &a.Parameters.CertificateName},
 		// TODO
 		// {Key: aws.String("apppack:appName"), Value: appName},
 		{Key: aws.String("apppack"), Value: aws.String("true")},
diff --git a/stacks/custom_domain_test.go b/stacks/custom_domain_test.go
new file mode 100644
index 0000000..dc5a790
--- /dev/null
+++ b/stacks/custom_domain_test.go
@@ -0,0 +1,22 @@
+package stacks
+
+import (
+	"testing"
+
+	"github.com/aws/aws-sdk-go/aws"
+)
+
+func TestCustomDomainStackName(t *testing.T) {
+	stack := CustomDomainStack{}
+	actual := stack.StackName(aws.String("example.com"))
+	expected := "apppack-customdomain-example-com"
+	if *actual != expected {
+		t.Errorf("Expected %s, got %s", expected, *actual)
+	}
+
+	actual = stack.StackName(aws.String("*.example.com"))
+	expected = "apppack-customdomain-wildcard-example-com"
+	if *actual != expected {
+		t.Errorf("Expected %s, got %s", expected, *actual)
+	}
+}