How do I add my name to the 'From' field in Apple mail?

When I imported my old e-mail accounts into Apple mail, the addresses in the from-field when I send mails appear with my name first, then a dash and then the e-mail address. This allows the receivers to see my name in their inboxes. But then I got an iCloud account, and the from-field when I use it only shows the e-mail address, and that's all the receivers see in their inboxes, too. The from-field does not seem to be editable, and I don't find any thing in the account settings enabling me to add my name. Can you help me?

[Re-Titled by Moderator]