How to send an email through an outlook.com alias email address on iOS?
I haven't found any actual answer for my question, but instead found a very good alternative.

Basically @icloud.com accounts also allow the creation of aliases that can be used in all iOS Mail apps, with one particular advantage: the alias allows changing the name of the recipient as well, something @outlook.com account aliases does not allow.

You can create @icloud.com aliases using the web interface options.