Sorry I am not from that region and do not know the court procedures. You can call your local district courts and ask them,
One thing I can tell you, you will not get name changed in local courts in 23 days. It takes 2-3 months in Atlanta region. You give an ad in local newspapers that has to be run for atleast 4 weeks.
The form you found says "UNITED STATES DISTRICT COURT" on the top, which means it goes to district court.
Search for "dustrict court" for your state/city, get the phone no, call the clark there. They can tell you which form to fill in and how to go about the name change. Alternatively, you can contact an attorney that can handle it for you.
In either case, I don't think you can get name changed this fast. Your best bet is to get the certificate, then apply for name change, get passport with correct name, then apply for replacement of cert with correct name (if you want to, not mandatory)
hope that helps