Basically, in your application, It is always recommended to use the id field that uniquely identifies the tenant.
The displayname, as the name indicates, it is for just displaying. Also, the display name property can be nullable, as per the specifications. As you can see, for not nullable, the documentation specifies it clearly.
See the specifications for the display name property
See the specification for another property that is not nullable.
So I recommend you to work with ID or the verifiedDomains field in your business logic to uniquely identify the organization.
Hope this helps