Sending, receiving, and organizing email in Outlook.com
Hello
If you go to your account https://account.live.com > Your info > Sign in preference, is your primary alias an outlook.com or hotmail.com alias?
This can happen if your account originally started with a non-Microsoft domain alias, meaning, it was originally set up with a third party email address, such as gmail, yahoo, etc. Because they are third party email, their actual email service is still with their providers like Gmail or Yahoo, and when it comes to outlook.com, they only served as username, but it doesn't have actual email functionality. And since outlook.com is the web mailbox for Microsoft account, so Microsoft would come up with a placeholder outlook.com address to label your mail box.
Even if you later added an outlook.com or hotmail.com alias, this mailbox name will stay. But your outbound email should carry the actual outlook.com or hotmail address. Unfortunately I don't think you can change that. I have the same problem too as I initially set up mine with gmail.com address. Years later, even though I have added an outlook.com alias, my mailbox still shows the random outlook.com address.
Regarding the desktop app issue, can you tell me more about it?