1. Prove you meet the conditions for changing it (you must show proof of identify _theft_ and how it disadvantages you)
2. Show up at an office, in person, with original documentation.
Sounds like a great startup idea: make fixing 143M citizens' identities as easy as ordering a pizza. Or create the Uber for people who will stand in line for you at the Social Security office.
[1]: https://faq.ssa.gov/link/portal/34011/34019/Article/3789/Can...