Name on MAIL

Hi!

Even though in my MAIL application (Both OS and IOS), I "told" my computer that my emails should read as coming from my very common nickname, the emails that I send show to the sender as coming from my complete name ... Which almost nobody knows! I don't know how to correct that. In the MAIL settings in iCloud.com it says "Tif", which is how I would like it to be. But still the emails are sent from my full name. Can anybody help?

Thank you