Add player names to snake display

Show human-readable player names instead of player IDs in both desktop
and web clients. Player names are now stored in the Snake model and
synchronized across all clients.

Changes:
- Added player_name field to Snake model
- Updated create_snake() to accept player_name parameter
- Desktop client shows "YOU:" or "PlayerName:"
- Web client shows "You (Name)" or "Name"

🤖 Generated with [Claude Code](https://claude.com/claude-code)

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

src/shared/models.py

@@ -34,6 +34,7 @@ class Snake:
     score: int = 0
     stuck: bool = False  # True when snake is blocked and shrinking
     color_index: int = 0  # Index in COLOR_SNAKES array for persistent color
+    player_name: str = ""  # Human-readable player name
 
     def get_head(self) -> Position:
         """Get the head position of the snake."""
@@ -49,6 +50,7 @@ class Snake:
             "score": self.score,
             "stuck": self.stuck,
             "color_index": self.color_index,
+            "player_name": self.player_name,
         }
 
     @classmethod
@@ -61,6 +63,7 @@ class Snake:
         snake.score = data["score"]
         snake.stuck = data.get("stuck", False)  # Default to False for backward compatibility
         snake.color_index = data.get("color_index", 0)  # Default to 0 for backward compatibility
+        snake.player_name = data.get("player_name", "")  # Default to empty string for backward compatibility
         return snake