diff --git a/internal/services/machinelearning/machine_learning_compute_cluster_resource.go b/internal/services/machinelearning/machine_learning_compute_cluster_resource.go
index 5193ca81381e..a8107149c9e4 100644
--- a/internal/services/machinelearning/machine_learning_compute_cluster_resource.go
+++ b/internal/services/machinelearning/machine_learning_compute_cluster_resource.go
@@ -16,6 +16,7 @@ import (
 	"github.com/hashicorp/terraform-provider-azurerm/helpers/azure"
 	"github.com/hashicorp/terraform-provider-azurerm/helpers/tf"
 	"github.com/hashicorp/terraform-provider-azurerm/internal/clients"
+	"github.com/hashicorp/terraform-provider-azurerm/internal/services/machinelearning/validate"
 	"github.com/hashicorp/terraform-provider-azurerm/internal/tf/pluginsdk"
 	"github.com/hashicorp/terraform-provider-azurerm/internal/tf/validation"
 	"github.com/hashicorp/terraform-provider-azurerm/internal/timeouts"
@@ -41,9 +42,10 @@ func resourceComputeCluster() *pluginsdk.Resource {
 
 		Schema: map[string]*pluginsdk.Schema{
 			"name": {
-				Type:     pluginsdk.TypeString,
-				Required: true,
-				ForceNew: true,
+				Type:         pluginsdk.TypeString,
+				Required:     true,
+				ForceNew:     true,
+				ValidateFunc: validate.ComputeClusterName,
 			},
 
 			"machine_learning_workspace_id": {
diff --git a/internal/services/machinelearning/validate/compute_cluster_name.go b/internal/services/machinelearning/validate/compute_cluster_name.go
new file mode 100644
index 000000000000..a00c68e96a8a
--- /dev/null
+++ b/internal/services/machinelearning/validate/compute_cluster_name.go
@@ -0,0 +1,24 @@
+// Copyright (c) HashiCorp, Inc.
+// SPDX-License-Identifier: MPL-2.0
+
+package validate
+
+import (
+	"fmt"
+	"regexp"
+)
+
+func ComputeClusterName(i interface{}, k string) (warnings []string, errors []error) {
+	v, ok := i.(string)
+	if !ok {
+		errors = append(errors, fmt.Errorf("expected type of %q to be string", k))
+		return
+	}
+
+	// The portal says: It can include letters, digits and dashes. It must start with a letter, end with a letter or digit, and be between 3 and 32 characters in length.
+	// If you provide invalid name, the rest api will return an error with the following regex.
+	if matched := regexp.MustCompile(`^[a-zA-Z][a-zA-Z0-9-]{1,30}[a-zA-Z0-9]$`).Match([]byte(v)); !matched {
+		errors = append(errors, fmt.Errorf("%s must be between 3 and 32 characters, may only include alphanumeric characters and '-' and must start with a letter, end with a letter or digit", k))
+	}
+	return
+}
diff --git a/internal/services/machinelearning/validate/compute_cluster_name_test.go b/internal/services/machinelearning/validate/compute_cluster_name_test.go
new file mode 100644
index 000000000000..ae729346b3c9
--- /dev/null
+++ b/internal/services/machinelearning/validate/compute_cluster_name_test.go
@@ -0,0 +1,89 @@
+// Copyright (c) HashiCorp, Inc.
+// SPDX-License-Identifier: MPL-2.0
+
+package validate
+
+import "testing"
+
+func TestComputeClusterName(t *testing.T) {
+	testData := []struct {
+		input    string
+		expected bool
+	}{
+		{
+			// empty
+			input:    "",
+			expected: false,
+		},
+		{
+			// basic example
+			input:    "hello",
+			expected: true,
+		},
+		{
+			// cannot start with a hyphen
+			input:    "-hello",
+			expected: false,
+		},
+		{
+			// cannot start with a digit
+			input:    "1hello",
+			expected: false,
+		},
+		{
+			// can end with a digit
+			input:    "hello2",
+			expected: true,
+		},
+		{
+			// cannot end with a hyphen
+			input:    "hello-",
+			expected: false,
+		},
+		{
+			// cannot contain other special symbols other than hyphens
+			input:    "hello.world",
+			expected: false,
+		},
+		{
+			// cannot contain underscore
+			input:    "hello_world",
+			expected: false,
+		},
+		{
+			// hyphen in the middle
+			input:    "hello-world",
+			expected: true,
+		},
+		{
+			// 2 chars
+			input:    "ab",
+			expected: false,
+		},
+		{
+			// 3 chars
+			input:    "abc",
+			expected: true,
+		},
+		{
+			// 32 chars
+			input:    "abcdefghijklmnopqrstuvwxyzabcdef",
+			expected: true,
+		},
+		{
+			// 33 chars
+			input:    "abcdefghijklmnopqrstuvwxyzabcdefg",
+			expected: false,
+		},
+	}
+
+	for _, v := range testData {
+		t.Logf("[DEBUG] Testing %q", v.input)
+
+		_, errors := ComputeClusterName(v.input, "name")
+		actual := len(errors) == 0
+		if v.expected != actual {
+			t.Fatalf("Expected %t but got %t", v.expected, actual)
+		}
+	}
+}