feat(account): give a fresh guest a distinct "Guest######" display name

Every guest showed a bare "Guest" to opponents (e.g. in a random match). Mint the display name
as "Guest" + a random six-digit suffix at provisioning, so guests are distinguishable. Not an
identifier and not unique — a label only, so collisions are harmless.

backend/internal/account/account.go

@@ -10,6 +10,7 @@ import (
 	"database/sql"
 	"errors"
 	"fmt"
+	"math/rand/v2"
 	"strings"
 	"time"
 
@@ -525,8 +526,13 @@ func (s *Store) create(ctx context.Context, kind, externalID string, seed provis
 	return created, nil
 }
 
-// guestDisplayName is the display name stamped on a freshly provisioned guest.
+// guestDisplayName mints the display name stamped on a freshly provisioned guest: "Guest" plus a
-const guestDisplayName = "Guest"
+// random six-digit suffix (e.g. "Guest042317"), so a guest is distinguishable to opponents — in a
+// random match the other player sees a distinct name rather than every guest reading a bare
+// "Guest". Not an identifier and not unique (collisions are harmless — it is a label only).
+func guestDisplayName() string {
+	return fmt.Sprintf("Guest%06d", rand.IntN(1_000_000))
+}
 
 // ProvisionGuest creates a fresh ephemeral guest account: a durable row carrying
 // no identity, flagged is_guest, so it can hold a session and a game seat (both
@@ -553,7 +559,7 @@ func (s *Store) ProvisionGuest(ctx context.Context, browserTZ, language string)
 	}
 	stmt := table.Accounts.
 		INSERT(table.Accounts.AccountID, table.Accounts.DisplayName, table.Accounts.IsGuest, table.Accounts.TimeZone, table.Accounts.PreferredLanguage).
-		VALUES(accountID, guestDisplayName, true, tz, lang).
+		VALUES(accountID, guestDisplayName(), true, tz, lang).
 		RETURNING(table.Accounts.AllColumns)
 
 	var row model.Accounts

backend/internal/inttest/account_test.go

@@ -5,6 +5,7 @@ package inttest
 import (
 	"context"
 	"errors"
+	"regexp"
 	"testing"
 	"time"
 
@@ -241,6 +242,10 @@ func TestProvisionSeedsTimeZone(t *testing.T) {
 	if guest.PreferredLanguage != "ru" {
 		t.Errorf("guest PreferredLanguage = %q, want the seeded ru", guest.PreferredLanguage)
 	}
+	// A guest's display name is "Guest" + a random six-digit suffix (distinct to opponents).
+	if m, _ := regexp.MatchString(`^Guest\d{6}$`, guest.DisplayName); !m {
+		t.Errorf("guest DisplayName = %q, want Guest + 6 digits", guest.DisplayName)
+	}
 	plainGuest, err := store.ProvisionGuest(ctx, "", "")
 	if err != nil {
 		t.Fatalf("provision plain guest: %v", err)