When setting up the first app in App Store Connect and entering in our company name it states:
"The company name that you entered is already in use."
However when using the iTunes search API and generally searching the app store, we cannot find any company/artist with the exacty company name we seek to use. There is no contact form to get in touch with Apple regarding this, even though we have a legal trademark, and someone has taken it for their company name.
The contact form allows you to have them call you based on.
Choose: 'membership and account', then 'other....', then schedule a phone call and have this conversation with that person.