Unable to update "Find My" email on MacBook

I changed my Apple ID email over a year ago, and now I want to reset my MacBook, but the "Find my" email showing is the old one. I didn't create a new apple id; I simply changed the email, yet it is showing the old ID. My password does not work on it, and there's no menu to click anything else. I need urgent help. Thank you.

[Re-Titled by Moderator]