Legal Name Change - Old name still showing up on sent emails

I have changed my legal name. I have done everything I am supposed to do, changed my Apple ID information, gone to iCloud.com to make sure I am sending with my new name. Yet my old name still shows up when sending email - even to people who would not have had my old name stored I.e. I have never sent them an email before. Example - old name Jane Doe, email address JD@icloud.com, new name Jacinda Doe, email address JD@icloud.com. When I send an email to someone who has never received an email from me the name appears as Jane Doe. This is not about an iCloud alias.