Lookup field shows the record's SFDC ID instead of its Name in My Accounts view.
In My Accounts view, the Primary Parent lookup field displays the record's 18-digit SFDC ID instead of the Name.
When the user opens the record's 18-digit SFDC ID in the browser, the following error occurs:
The user does not have access to the record itself.
In order to display the record's name in the lookup field, grant the user access to the record.
CRM Help Documentation: Account Lists and Views