Twitter does not yet integrate ENS names, or verify them, so setting them as your Twitter name is simpler than it first appears. All you need to do is to edit your name and enter it in!
Edit your Twitter profile
Go to Twitter and click on your Profile
Click the Edit button in the upper right of your profile page to edit it.
Type in your ENS name in the Name field
Press Save to save it.
That's it! You're done and should now be sporting your ENS name on Twitter!