Azure AD connect advise

Adedolapo Oyekanmi - Have you done the "custom domain" portion in the O365 Admin Portal? You'll need to check with your domain provider for exact steps on how to add a .txt record to you DNS to verify that you own the domain name so it will be exposed for use in O365. Then you can modify the settings and make "uni.edu" the default instead of "onmicrosoft.com" so the users emails will then look like what you want. 

https://docs.microsoft.com/en-us/office365/admin/setup/add-domain?view=o365-worldwide 

You might also have to modify the addresses of each existing users since this potentially was not completed before adding users.