Mismatch between Apple ID name

Hi, there is a mismatch between my name on Apple ID and the name which appears on my e-mails I send out.

My Apple ID name is X (which is aligned with my iCloud account name formation)

I use my iCloud mail account - X.SURNAME@icloud.com

However when I send emails people receive them with my old name Y (the name which appears when the new email pops up in your inbox)

Is it possible to fix this issue?

Thanks!