This is my order (if I remember correctly):
Australian Birth certificate - Name Only
Court Order Name Change State of Wisconsin - Name Only
Work/Payroll/Medical/Dental, Vision - Name Only (I hadn't gone fulltime at this point, but HR knew of my transition)
Social Security - Name Only
Drivers License - Name and Gender (Updated car title at the same time)
Dept Homeland Security - Name Only
USA Passport - Name and Gender
Australian Passport - Name Only
Mortgage, Banking, Credit Cards, Utilities, Rental Car, Frequent Flyer Programs, Gym Membership - Name Only
A lot of paperwork, not really, it all about organization skills. Develop your transition plan and execute!