Why couldn't you set the variable as private and use it throughout the project?

public class MainActivity extends AppCompatActivity {

    private EditText mEditText;
    private Button mStartButton;
    private String mName;

    @Override
    protected void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);

        mEditText = (EditText) findViewById(R.id.nameEditText);
        mStartButton = (Button) findViewById(R.id.startStory);

        mStartButton.setOnClickListener(new View.OnClickListener() {
            @Override
            public void onClick(View view) {
                mName = mEditText.getText().toString();

                if (mName.matches("")) {
                    Toast.makeText(MainActivity.this, "Please enter a valid User name", Toast.LENGTH_LONG);
                    return;
                } else {
                    startStory(mName);
                }
            }
        });
    }

    private void startStory(String mName) {
        Intent intent = new Intent(this, StoryActivity.class);
        intent.putExtra("UserName", mName);
        startActivity(intent);
    }