How do I change my name on my iCloud account?

We are talking about your first name and last name, not the e-mail address of your Apple ID., aren't we?

I just did a test of my Mac (macOS Sonoma 14.4.1): clicking on System Settings > [my name] > Personal Information > Name brought up the request of the Apple ID password, I entered it and then... nothing happened. I clicked a second time on "Name" and then a window popped up where I could modify my first name and last name.

Go to Apple ID to change your name: https://appleid.apple.com/account/manage/section/information.

That's odd, I can. Try to do it on a device. On an iPhone for instance, go to Settings > [your name] > Personal Information > Name.

The personal information section does not allow me to change the name on my Apple ID. I only have access to change Country, Language, and Reachable At information. Any other ideas?

I've also tried it on the only trusted device listed on my account (My MacBook Air) and there is no option in the system preferences to change my name.