Allow role to add a new record but not modify/delete existing records

Are you trying to limit editing of a particular field or the whole record?

Just one field- so a user could add a record to the Customer table with Name field: ABC Inc.. However, that same user wouldn't be able to change the Name. Fields like Address, Phone, etc would ok to modify. 

We're using a report from this table to update a SQL database, and I need the Name field to remain consistent once created. 

I would make a formula numeric field called [Record ID# mirror] with a formula of [Record ID#] 

Then make a dynamic form rule

when [Record ID# mirror]  > 0
make read only [customer name]

In Add mode that field will be zero or maybe blank.  But once saved, then the name field will not be editable. however, that will not prevent Grid Edit.

That would be a separate question.

Thanks! I ended up using a form rule: when date created is on or before the current date then make read-only Company Name

Is not ideal that users can still change customer names in grid edit, but it's a start.