I requested that the notice in the paper be waived, and the judge obliged. I was not required to publish my name change at all. There was also no hearing. NY.
I filled out the petition. Included a letter from my therapist explaining my situation and requesting that the publication be waived. Paid my $210.00. Submitted the paperwork. Waited about 5 days, got a manila envelope in the mail with the order. I went downtown, had copies made. Then proceeded to change my name on EVERYTHING!
If you include a letter from your therapist, get it notarized.
EDIT
Actually, I don't remember if the order came in the mail, or a letter saying that the name change was approved. Either way, the manila envelope had all the stuff I submitted, and I still had to go to the clerks office to get copies.