Permissions Management for Required Fields

Permissions Management for Required Fields

I want to be able to allow some users to edit some fields on accounts or contacts, but not other fields. It seems I am unable to set reader permission on the Account Name field and as a result the end users will need to be read only because we cannot have them editing Account Name. 

Is there a way to set granular permissions on a required field beyond a general read writhe for contacts or accounts?