I live in Australia, so YMMV, but for me, the things I needed to update were:
- Government/their services and programs, local and federal
- Medical things (insurance,, doctors, etc)
- Banks/Financial Institutions (I don't know how a 401k works, but that probably is included)
- Insurance
- Car registration
- Identity documents
- Wills, if you have one
- Company registrations, if you have one
Beyond that legal obligation, there is no one you have to tell if you don't feel comfortable. I took the opportunity of legally changing my name to finally come out in the rest of my life (work and uni), but you don't have to.