Correct, you need to use "personne" in this case but you have to change the sentence slightly for it to be correct (it is "faire confiance à q.n.")

"Elle ne fait confiance à personne"

"Because the negation surrounds the main conjugated verb?": You cannot just use "personne" just in place of "pas", if that is what you mean.

https://kwiziq.learnfrenchwithalexa.comNe ... personne = No one/nobody (French Negations)

Just to complement Christian's answer:

Personne and rien are not merely negation particles they also function as pronouns and hence can replace either the subject, the direct object or an indirect object:

Personne ne m'aime! -- Nobody loves me! (subject)
Je n'aime personne! -- I love nobody (direct object)
Tu ne parles à personne. -- You don't talk to anybody (indirect object)

Thanks a lot for these explanations, Christian and Chris!