feat(account): add /account/update_name endpoint

Implements POST /account/update_name — writes Viewer.DisplayName and
returns an empty array per the prod capture. Includes TDD test covering
the persist side-effect.

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

SVSim.UnitTests/Controllers/AccountControllerTests.cs

@@ -0,0 +1,34 @@
+using System.Net;
+using System.Text;
+using System.Text.Json;
+using NUnit.Framework;
+using Microsoft.EntityFrameworkCore;
+using Microsoft.Extensions.DependencyInjection;
+using SVSim.Database;
+using SVSim.UnitTests.Infrastructure;
+
+namespace SVSim.UnitTests.Controllers;
+
+public class AccountControllerTests
+{
+    [Test]
+    public async Task UpdateName_writes_display_name()
+    {
+        using var factory = new SVSimTestFactory();
+        long viewerId = await factory.SeedViewerAsync(tutorialState: 0);
+        using var client = factory.CreateAuthenticatedClient(viewerId);
+
+        var requestJson = """{"name":"littlefootse","viewer_id":"0","steam_id":0,"steam_session_ticket":""}""";
+
+        var response = await client.PostAsync("/account/update_name",
+            new StringContent(requestJson, Encoding.UTF8, "application/json"));
+
+        Assert.That(response.StatusCode, Is.EqualTo(HttpStatusCode.OK));
+
+        // Verify persisted name.
+        using var scope = factory.Services.CreateScope();
+        var db = scope.ServiceProvider.GetRequiredService<SVSimDbContext>();
+        var viewer = await db.Viewers.FirstAsync(v => v.Id == viewerId);
+        Assert.That(viewer.DisplayName, Is.EqualTo("littlefootse"));
+    }
+}