One issue that frequently comes up with new Office 365 Hybrid environments is that usernames do not synchronize properly between the on premises Active Directory and the Office 365 Tenant. If this happens you will see something resembling :
the source of this is usually that your primary UPN suffix in Active directory is different from your primary domain SMTP address or primary domain. This is very common as once upon a time it was recommended to name your internal AD domain differently from your primary smtp domain and use split dns for routing.
To fix this, you need to either change the UPN suffix for the user in question on the account tab in AD Users in Computers, or if that is not available, you will need to add the UPN suffix.
To add the UPN suffix, open AD Domains and Trusts, right click the top of the tree and select properties.
Open the UPN Suffixes tab, and then type the name of the DNS UPN Suffix you wish to add.
Click Add, and then click OK.
You will now have the new UPN suffix available to assign to your users.
Once you have assigned the UPN suffix to the problem user(s), initiate a directory sync with Azure AD, and the user names will now line up properly between the Office 365 Tenant and your on premises Active Directory.
Josef Hanning, PEI