Termination of the obligation of bail has become known as “exoneration.” Once the criminal case is resolved (criminal proceedings terminated or the surrender of the defendant into custody), the depositor or surety is relieved of their obligation and is entitled to return of the deposit.
Your New York bail lawyer will counter the prosecutor's arguments by giving reasons that you should be released without having to post bail (ROR), or that you should have to post a low bail. Ultimately, the judge will decide whether or not bail is required and if so, the amount.
And while some will tell you that you can't remain anonymous, the short answer is actually yes, you can. (But with one major consideration.) The Court is going to need a name and person to return the bond to once the court date has been successfully completed.
When bail is exonerated it means you or the bail bondsman gets their deposit back from the court clerk. When the defendant is exonerated, it means the charges are dropped and the defendant is no longer suspected of any wrongdoing. Last but not least, it is possible for bail exonerations to be denied.