The beta web-site wallet is available. Limit transactions to small amounts only please.https://wallet.bitshares.org
If you want to grab a account name, it should be quite easy. Accounts are reserved on the public blockchain and are first-come first-serve... I think it will become quite useful to you as there are projects being developed based on BitShares for: voting, gaming, music. Then on the business side, SEC compliant stock offerings for companies (not just the large ones anymore). Today, BitShares are used as money (market pegged assets), bearer shares (bitshares), and for its user issued assets (users issue there own shares).
You can register accounts with the wallet (if you send it some funds) or you may use the built-in faucet. In both cases, the account is registered as a public account.
For the newcomer: use a test transfer from any new source (line an exchange). The technical explanation is: make sure that anyone sending to a public account is using a recent version of full-wallet (like 0.6.1) or using the light wallet or this hosted-wallet. Older versions of the full client will send a private TITAN transaction instead of a public transaction. A full-node will be required to recover the TITAN transaction should this happen.
Source code, bugs, requests, etc.. are hosted at: https://github.com/bitshares/bitshares-js