Translating aa name to chinese is much trickier than it may seem. The chinese symbols aren't letters that represent a sound, they represent a meaning. You might have the same name tanslated with symbols that represent things such as beauty, power, brightness, etc, or translated with symbols tat represent stuff like stink, weakness, ugliness, etc, because the pronounciation of the sysmbols is the same while the meaning is completely different. It's best to go to someone chinese and let him give you different ways to spell your name and you choose what meaning you like best.
To answers your question, yes, 费德里科 is indeed a correct way to translate Federico.