feat: add service name to app-server (#12319)

Add service name to the app-server so that the app can use it's own
service name

This is on thread level because later we might plan the app-server to
become a singleton on the computer

codex-rs/app-server/tests/suite/v2/thread_start.rs

@@ -146,6 +146,34 @@ model_reasoning_effort = "high"
     Ok(())
 }
 
+#[tokio::test]
+async fn thread_start_accepts_metrics_service_name() -> Result<()> {
+    let server = create_mock_responses_server_repeating_assistant("Done").await;
+
+    let codex_home = TempDir::new()?;
+    create_config_toml(codex_home.path(), &server.uri())?;
+
+    let mut mcp = McpProcess::new(codex_home.path()).await?;
+    timeout(DEFAULT_READ_TIMEOUT, mcp.initialize()).await??;
+
+    let req_id = mcp
+        .send_thread_start_request(ThreadStartParams {
+            service_name: Some("my_app_server_client".to_string()),
+            ..Default::default()
+        })
+        .await?;
+
+    let resp: JSONRPCResponse = timeout(
+        DEFAULT_READ_TIMEOUT,
+        mcp.read_stream_until_response_message(RequestId::Integer(req_id)),
+    )
+    .await??;
+    let ThreadStartResponse { thread, .. } = to_response::<ThreadStartResponse>(resp)?;
+    assert!(!thread.id.is_empty(), "thread id should not be empty");
+
+    Ok(())
+}
+
 #[tokio::test]
 async fn thread_start_ephemeral_remains_pathless() -> Result<()> {
     let server = create_mock_responses_server_repeating_assistant("Done").await;