This is my MO:
I am yet to go to Brazil but when travelling to countries where US passport holders do not require visas (such as Brazil currently), I buy the ticket on my US name and only use the US passport. I do believe however that you would need to present your Brazilian passport at immigration (PF).
When a visa is required for US passport holders but not Brazilian, I still book the trip under my US passport name, but at the check-in, I present my Brazilian passport along with a copy of the name change disposition and present my Brazilian passport at the destination. So far I have had no issues with any airline as they seem to have standard procedures for this scenario.
I am not sure if what @aaron2020 says is correct about the Brazilian passport becoming invalid, but I do know that it is not straightforward to have your original name changed in Brazil. There is precedent but at the same time, there is an interpretation of the Brazilian law that leads to person requesting it losing citizenship altogether. In any case, if you want to give it a try, the first thing to do is to contact a specialized lawyer in the state where your ID (Carteira de Identidade) was issued.