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 the basics of name changes and/or sex designation and provides a DIY Form
New York State Department of Health, Department of Vital Records explains how to amend birth certificates.
The laws on name changes are in Civil Rights Law, art 6 Change of Name