Should company name show for former Prim Admin/now Company Admin when logging in with their own email address? No company name shows for Company Admin when logging in?

Yes, PCTW. The company name will display when your company admin logs in to QuickBooks Online using their email address.

Since you mentioned that the company name is not appearing on the company admin side, we can verify if they have the appropriate permissions to access the account and check whether the associated email address is correct.

To begin, ask your current primary admin to log in and check whether the company admin is listed among the users and has the correct role.

Here are the steps they can follow:

1. Head to the Gear icon, then select Manage users.
2. Verify that they have the Company Admin role assigned and confirm if the email is accurate.

If the email is incorrect, the primary admin can re-invite the company admin by deleting and re-adding them with the correct details. Please see the attached screenshot for visual reference. 
 

Once added, the company admin will receive an email invitation to accept their role. 
 

For a detailed overview of each user role in QuickBooks, including their access levels, you can read the article: User roles and access permissions. 
 

Also, I recommend exploring our QuickBooks Live Expert Assisted service. Our team of knowledgeable professionals is ready to help you navigate the features of your plan and efficiently set up your users, accounts, customers, and vendors.
 

This thread will remain open, so if you have further questions, we're still here to assist.