How do I change my name or my child's name?

What is the difference between changing a name and correcting a name on a birth certificate?
Must I change my name when I get married?
How do I change my name after a divorce?
How do I change my name after becoming a US citizen?
Where do I find the law on name changes?

Answer

A name is changed on a birth certificate when there has been a legal name change or adoption.
A birth certificate is corrected because of a typographical error.
CourtHelp explains how to get a court order for a name change and provides a DIY Form
CourtHelp explains Child Name Changes and provides a DIY Form
CourtHelp explains name changes after marriage, divorce, adoption, and citizenship.
The laws on name changes are in Civil Rights Law, art 6 Change of Name