There is no easy way of getting rid of multiple accounts. One might do like eBay and send some kind of confirmation codes by "real" mail to an existing address and ask for some kind of proof of identity, then you will have to get another house for your next account. Or play as your wife/husband/daughter/brother/sister/son/grandma/grandpa.
That solution would make most people think twice before playing this game with the first account...
Another way would be to "hitch hike" on someone that is doing a pretty good job of tracking multiple accounts, like Facebook. Facebook login.
That solution would scare off people that does not have Facebook.
No, I think the only solution is to make sure that you do not win anything on creating a new account. Do not allow hacks to enter tournaments for instance. Maybe Tour Pro should be lower the limit if you want to enter tournaments where you can win credits and if you want to play Challenge.
The level system is good, it forces you to suffer while you level up, but the suffering should be increased with the added "no tourny" option. Note that this would not affect "real" newbies, they have their hands full learning the game and will not win any tournaments anyway. There can be amateur tournaments without prizes maybe.
The tier system needs adjustment. It is far too easy to advance up to Tour Pro and even Master. Master => Tour Master => Legend seems reasonable, you really need to make an effort there (I have not managed yet), but Hack => Amateur => Pro is done in a few days if you put your heart into it.
Then there is the dreaded Legend status. Why is that a punishment? One should treat the Legends well! First of all, I think there is too many legends in this game. Tour Master should be the top tier IMHO and Legend should be honorary. Reserve the long tees for Legends only tournaments and allow legends to play from the same tee, with the same green speed, as the Tour Master.
A Legend should be a Tour Master who have earned his status in a different way than just working his average below 61 or whatever it might be. Maybe by winning a lot of tournaments, maybe by hitting 3 HIO in one round.
Do not punish the Legends by forcing them to look silly shooting from a tee 100 yards behind the others.
Then they stay. Then they are not tempted to create a new account.
As a summary:
-Block players below Tour Pro from prize tournaments
-Make it more difficult, and time consuming (not necessarily by games played but at least by days spent) to advance to next tier
-Make Legend a honorary status with extra benefits, not a punishment as it is now.