fix(robot): show the per-game name in REST game views, not the account name

The seat display-name snapshot only reached the live-event path (seatNames);
the REST DTO layer still resolved seat names from the account store
(fillSeatNames), so the game screen and lobby list showed the robot's seeded
account name ("Женя") while the your_turn toast showed its per-game name
("Звёздный_Барс2"). Carry the snapshot into gameDTOFromGame and have
fillSeatNames fall back to the account only for a seat with no snapshot (a
pre-snapshot legacy row). Friends and invitations keep account names (the
persistent identity, not a per-game disguise).

backend/internal/server/dto.go

@@ -77,8 +77,9 @@ type moveRecordDTO struct {
 	Total   int       `json:"total"`
 }
 
-// seatDTO is one seat's public standing. DisplayName is resolved from the account
-// store by the handler (the game domain keys seats by account id only).
+// seatDTO is one seat's public standing. DisplayName is the seat's display-name snapshot
+// (the per-game name, frozen when the seat was taken); fillSeatNames fills it from the
+// account store only when a seat has no snapshot yet (a pre-snapshot legacy row).
 type seatDTO struct {
 	Seat        int    `json:"seat"`
 	AccountID   string `json:"account_id"`
@@ -199,19 +200,21 @@ const awayTimeLayout = "15:04"
 func gameDTOFromGame(g game.Game) gameDTO {
 	seats := make([]seatDTO, 0, len(g.Seats))
 	for _, s := range g.Seats {
-		// An open game's still-empty opponent seat has no account: emit an empty id (the
-		// display name is left empty by fillSeatNames) so the client shows "searching for
-		// opponent" rather than the nil-UUID.
+		// An open game's still-empty opponent seat has no account: emit an empty id (and an
+		// empty display name) so the client shows "searching for opponent" rather than the
+		// nil-UUID. DisplayName carries the seat's per-game snapshot; fillSeatNames fills
+		// only the seats still without one from the account store.
 		accountID := ""
 		if s.AccountID != uuid.Nil {
 			accountID = s.AccountID.String()
 		}
 		seats = append(seats, seatDTO{
-			Seat:      s.Seat,
-			AccountID: accountID,
-			Score:     s.Score,
-			HintsUsed: s.HintsUsed,
-			IsWinner:  s.IsWinner,
+			Seat:        s.Seat,
+			AccountID:   accountID,
+			DisplayName: s.DisplayName,
+			Score:       s.Score,
+			HintsUsed:   s.HintsUsed,
+			IsWinner:    s.IsWinner,
 		})
 	}
 	last := g.TurnStartedAt

backend/internal/server/dto_test.go

@@ -1,6 +1,7 @@
 package server
 
 import (
+	"context"
 	"net/http"
 	"testing"
 	"time"
@@ -111,3 +112,35 @@ func TestMoveRecordDTOFrom(t *testing.T) {
 		t.Fatalf("move dto mismatch: %+v", dto)
 	}
 }
+
+// TestGameDTOCarriesSeatSnapshot checks the DTO carries each seat's display-name
+// snapshot (so a disguised robot's per-game name reaches the REST views, not just live
+// events) rather than leaving it for an account lookup.
+func TestGameDTOCarriesSeatSnapshot(t *testing.T) {
+	g := game.Game{
+		Variant: engine.VariantEnglish, Players: 2, TurnTimeout: time.Hour,
+		Seats: []game.Seat{
+			{Seat: 0, AccountID: uuid.New(), DisplayName: "Звёздный_Барс2"},
+			{Seat: 1, AccountID: uuid.New(), DisplayName: "Тест"},
+		},
+	}
+	dto := gameDTOFromGame(g)
+	if dto.Seats[0].DisplayName != "Звёздный_Барс2" || dto.Seats[1].DisplayName != "Тест" {
+		t.Fatalf("seat snapshot not carried into DTO: %+v", dto.Seats)
+	}
+}
+
+// TestFillSeatNamesKeepsSnapshot checks fillSeatNames leaves a seat whose snapshot is
+// already set untouched (no account lookup), so the per-game name is not overwritten by
+// the robot's seeded account name.
+func TestFillSeatNamesKeepsSnapshot(t *testing.T) {
+	s := &Server{} // accounts is unused: a present snapshot must skip the lookup
+	dto := &gameDTO{Seats: []seatDTO{
+		{Seat: 0, AccountID: uuid.New().String(), DisplayName: "Звёздный_Барс2"},
+		{Seat: 1, AccountID: uuid.New().String(), DisplayName: "Тест"},
+	}}
+	s.fillSeatNames(context.Background(), dto, map[string]string{})
+	if dto.Seats[0].DisplayName != "Звёздный_Барс2" || dto.Seats[1].DisplayName != "Тест" {
+		t.Fatalf("fillSeatNames overwrote a seat snapshot: %+v", dto.Seats)
+	}
+}

backend/internal/server/handlers_game.go

@@ -66,10 +66,15 @@ type complaintRequest struct {
 	Note string `json:"note"`
 }
 
-// fillSeatNames resolves each seat's display name from the account store, memoising
-// across seats and games within one request.
+// fillSeatNames fills each seat's display name from the account store — memoising across
+// seats and games within one request — for the seats that carry no per-game snapshot yet
+// (a pre-snapshot legacy row). A seat whose snapshot is already set is left untouched, so
+// a disguised robot keeps its per-game name rather than reverting to its account name.
 func (s *Server) fillSeatNames(ctx context.Context, g *gameDTO, memo map[string]string) {
 	for i := range g.Seats {
+		if g.Seats[i].DisplayName != "" {
+			continue // the seat already carries its per-game snapshot
+		}
 		id := g.Seats[i].AccountID
 		name, ok := memo[id]
 		if !ok {