When You can see Your client's name in AppStore Connect (https://appstoreconnect.apple.com), but not on Apple Developer portal (https://developer.apple.com), this means that Your client created his account as an Individual.
To check his account type, client should go to his developer account, and then check the Entity type
in the Membership
section:
After he confirms that his Entity type
is set to Individual, he can request to change it in one of the following ways:
Go to this contact form (linked above) and fill in all the data (Region, Name, Website, D-U-N-S Number etc.). You can get to this form "manually" by clicking Need to edit this information?
in the bottom right corner of the Membership
section. I would recommend You to use this form, because Apple then won't have to contact You for any of the Organization's information after Your submission.
Go to this contact form (linked above), select Account updates and renewals
and in the Message
field write something similar to this:
I’d like to convert my account from Individual to Organization.
This will be our only Organization account.
Here are the information regarding the company:
CEO/Director Name: First and Last Name.
Company Name: Your Company Name, including Ltd or Inc.
Account Type: Organization.
D-U-N-S Number: your Company’s DUNS number.
Address: Your Company’s Legal Address.
Phone Number: Your mobile phone or another phone number where you can be reached
According to this Quora answer, transition process can take around 7 days to complete, so be patient. :)