User Profile Services (UPS) exists in SharePoint to sync user objects' titles, but does not appear to update groups' titles. This will cover a user changing their name (married, etc.), however, the UPS does not sync group name changes.
The AD group display name is kept in SQL and therefore is unaware of AD changes. It has no push notification. However, PowerShell scripts could be leveraged by looping all sites with unique permissions, find groups, compare SID to AD, and update local SPGroup if name is different.
Thanks to Jeff Jones for his input on this as well..