A Hyphenate name is a family name with two parts, which may or may not have a hyphen in it. Helen Richardson-Walsh for example has the family names separated with a hyphen. Names like this are called double barreled name.
The rules around getting your name Hyphenate are similar to those you would follow if you were getting a name changed after marriage.
Notify your employer, banks and government agencies of your legal name change. The court order can be shown to the Social Security Administration, Department of Motor Vehicles, United States Passport agency, the IRS, Voter Registration, credit card companies and utility companies as proof of the new Hyphenate name.