I've been plagued by this issue many times:
If I add a contact in Android (5.1.1 SliM ROM), it gets synched to my Google Contacts as it should. But if I change the name in Google Contacts, this change will not be reflected in Android contacts, even when all other info (phone, mail, etc.) are synched correctly.
It seems that Android is storing names in a field that is not editable from Google Contacts? How can I make sure Android and Google show the same names?