Scenario: User profile property(last name) in your organization’s Active Directory was edited for a user/set of users but, the change is not reflected in SharePoint Online site collection.
Why? I can think of two reasons;
Reason 1-Your site collection loves the user(s) old profile property so much that it refuses to let go of it.
Reason 2. User(s) is not flagged as active on the site.
As much as I want to believe that reason 1 is right and my SharePoint site adores me, it definitely is not the case. Unfortunately SP is not evolved enough to have biologically based emotions. I know, bummer! That leaves us reason 2.
Lets look at AD profile sync in SharePoint and Office 365.
SharePoint online automatically does a one way sync from AD->O365->SharePoint every 24 hrs(default setting). If after the sync the profile still displays old info, you can remove user and add them again in site collection.
To remove user from all users group, go to gear icon on top right of O365-> Site Settings ->People and Groups(under Users and Permissions section).
Select the URL, replace MembershipGroupID=xyz with MembershipGroupID=0(yoursharepointsite url/sites/site collection name/_layouts/15/people.aspx?MembershipGroupID=0)
Select and remove the incorrect user(s) from the group and re-add them again. The updates the underlying userInfo table which inturn updates your site collection user info.