How Would I Change My Name As A Dual Citizen?

I’m a dual citizen of the US and Portugal, currently living in Portugal but I was born in the US (CT). I want to change my first name but i’m extremely worried about accidentally commuting identity fraud in one country. To the best of my knowledge I have to be in the country i’m changing my name in for court proceedings for the duration of the process, but i’m worried about flying between countries in the middle of the process while my passports and IDs don’t match. How do I go about this without committing an international crime? Is there a way to change my name without traveling back to the US?