The onmicrosoft.com alias in 365 in some situations can be set incorrectly as a primary email address on an account. This will show any received emails from this account showing with the .onmicrosoft domain rather than what the users actual domain should be.
Assuming that this cannot be changed manually in 365 because AD sync is active the following checks need to be made.
In AD;
- On the users account properties > General > Email
- Ensure the correct and intended email address has been set here
- On the users account properties > Attribute Editor > proxyaddresses
- Double click to open attribute editor > Value to add: SMTP:example@domain.com
(Ensure that the value to add is copied exactly how it shows above, the lack of spaces is intended.)
- Click 'Add' > 'OK' > 'Apply'
- Next sync should change this in 365.