Sending, receiving, and organizing email in Outlook.com
I did as suggested in this forum (Send emails from alias in Outlook 365 Web - Microsoft Community) I have ticked the option to "turn on sending from aliases" on Exchange > Settings > Mail Flow > General, as it was not ticked before. At the time it didn't seem to work, but 24h later it was working as expected.
I also saw this one (Send from alias in Outlook 365 web - Microsoft Community) where they suggest updating "Addresses to send From" but I also cannot see this field when I look at my Outlook Settings > Email > Compose and Reply. Nonetheless, the first one seem to have done the trick for me.