It is very difficult to get a new trial. After conviction, you would have to appeal and the odds of the court of appeals overturning your conviction are tiny. Get an attorney you trust before your trial!
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It is impossible to answer your question because you haven't mentioned the reason for the new trial. If on appeal your public defender was found to be ineffective at trial you would most likely be assigned an new attorney from the PD's Office. However, there are other reasons why you might be awarded a new trial which may not allow you to receive another assigned lawyer. I suggest that you speak to several experienced attorneys and hire the one you feel most comfortable with. Good luck!.
The big problem with your statement is "I was granted a new trial if I don't like how I was represented." I'm not sure if you just phrased it in a bad way, but you DO realize that you can't just get a new trial because you didn't like the way the lawyer tried your case, right? You would have to show that the things your attorney could have done differently would have had a fundamental impact on your trial. Put another way, just because you didn't like your lawyer's strategy doesn't mean you would have been acquitted if he did things your way, and unless that's the case you'll be hard-pressed to get a new anything on your case.
I agree with what other attorneys have said. If you're going to go to trial, do it with a lawyer who sees things the way you do (though I would note that if multiple attorneys all tell you the same thing that you disagree with, perhaps it's time to visit WHY they're all saying the same thing.)
It's unwise to bank on a jury conviction being overturned on a motion for new trial. While it does happen sometimes, ineffective assistance of counsel ("IAC") is a high hurdle to jump.
You may also want to consider where you'll be (in prison, in jail, on probation?) if convicted and seeking a new trial. While it is sometimes possible to obtain a new trial in post-conviction proceedings in the circuit court, this can easily take several months. Appeals to the court of appeals can easily take a year before a decision is issued.
That said, the SPD would appoint private counsel to represent you if you were granted a new trial on the grounds of ineffective assistance of counsel and you still qualified for SPD representation.
Do not wait for the appeal to start taking your defense seriously. You have a right to fire a public defender and retain a lawyer of your choosing at any time. I recommend it!