My wife is a Brazilian citizen (I am a US citizen), and we wanted to begin the process of applying for a green card for permanent residency in the US. Right now, she is an F-1 student visa with 1-year OPT. As part of this process, we also wanted to change her name.

Should we change her name before starting the process in Brazil? In the US? Or both? Or, should we apply for the green card under her current name and then change it once the process is complete?

All of her current documentation and IDs (visa, passport, OPT card, driver's license, social security card) uses her current name. The only thing that has her new name is our marriage certificate.