Apple email sender name different to people who don’t have me as contact/Outlook

When I was a kid, I messed around with some settings (I don’t remember which) and named my Apple ID name Jesse. I tried to fix it recently because when I send an email about a school project to my teachers for example, it shows up as Jesse Vu on their end. I’ve tried going into iCloud and Apple ID settings but when I changed my display name/sender name, it still showed up as Jesse Vu when I tested it with my mom. How can I change the name? Please let me know, this is a very annoying problem.