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!
Its always discouraging to see people exploiting legitimate means of advertisement in other to build the business to the point of acceptance by the community and the unwholesome part of it is that such individual won't use such faucets to play thereby totally defeat the very essence of why the faucets is launched in the first place. Its unfortunate that there is no way to stop it as every form of suggestions has a loophole that can be exploited for this selfish reason.
However, there is a potent way I would subscribe to in other to ensure the act is frustrating and that is by reducing the amount that can be claimed within the amount to the least unit of Satoshi with that, faucets abusers would be discouraged because it would mean investing much time to earn little which would make it available for newbies trying to earn and the sense of wagering to earn more, would make them visit the site to try their luck.