1. Can we finalize a person for an event or competition?
Do we only finalize issue?
2. Can we say: I have to finalize somebody for the position of trainer by thursday.
Finalize is a neologism in English and, in my opinion, is best not used.
You canīt finalize a person (unless you kill him;) Iīve heard it used most frequently as it relates to a topic under discussion.