How can I create unit test for this method?

How can I create a unit test for this service:

public class UserService {

    private Map<String, User> userStorage = new HashMap<>();

    public void saveOrUpdate(User user) {
        User userFromStorage = userStorage.get(user.getId());

        if (userFromStorage == null) {
            userStorage.put(user.getId(), user);
        } else {
            userFromStorage.setName(user.getName());
            userStorage.put(userFromStorage.getId(), userFromStorage);
        }
    }
}

How can I check that user creates or update successfully?

I can change void to User and return updated user and create this:

assertEquals(user.getName(), updatedUser.getName())

But what if I can't change method signature? How can I test it?