Managing personal Outlook.com account settings, security, and privacy
@عبدالله بدر محمد الحمودي said
it sends me an email saying i should click on a link that verify the email ... but after doing so nothing happens
Sounds like you are hung up on the Add Alias page https://account.live.com/AddAssocId
Not the Make Primary page https://account.live.com/names/manage
If you are not getting the verification email to the account you are trying to add as an alias:
Try sending that email address a normal email from your Outlook client. Does it get delivered? (i.e. Is the email valid?)
Check the Junk/Spam folders for the email you are trying to add as an alias. The verification emails come from a Microsoft Service (not your existing account email). Might be getting blocked.
And be aware that even once you get it added as an Alias, you may run into problems trying to promote it to Primary.
https://learn.microsoft.com/en-us/answers/questions/5997647/how-to-make-a-different-email-the-primary