Presumably a feature like high scores should be implemented in its own class, rather than included in the "main" class.
Good object-oriented design involves splitting up the responsibilities among different classes, with each class having responsibilities that match its name. Perhaps you need a HighScoresTable class, and should think about which methods it needs -- perhaps something like this:
- List getRankedListOfNames()
- List getRankedListOfScores()
- void addNewScore(String name, int score)
and naturally, you'd need some private fields to store the high scores data.