Not so long ago, we simplify registration process at our site leaving only the username field...
As a consequence, we are faced with a problem of creating multiple accounts by the same user and abusing faucet (faucet at our site - 0.007 mBTC and only request every 3 hours when balance is zero).
Guys, what solutions do you recommend?

Thank you!
Some recommendations for you:
Email registration only (fill in email addresses and send the login links)
Phone registration only (not recommended)
That's something I can think about.