I would suggest your customer, not you, Use the contact form to contact support. https://www.dreamhost.com/support/ They will likely need to email back at the address the account is registered under, so the customer will then need to find which email address has the reply waiting. They likely won't just hand out the info in a reply, that would in fact breech privacy and potentially be a security risk. Whatever the method dreamhost does have a protocol and they will not stray for it. If they even in the remotest possibility think the request might be fraudulent they will not reply, doing so might be a breach of privacy. If the customer knows the credit card number used with the account include the first and last 4 digits with the request and I'm sure that will help, but again they will likely not reply to an email that's not associated with the account.
Dreamhost protects the customers private data and typically will not reply if the person contacting might be an ex-employee, estranged spouse etc. this is why I included the words "not you" in the paragraph above.
Also for a request like this one, expect it will be dealt with during 9-5 mon-fri (GMT-8) business hours. Typically the 24/7 support staff won't be equipped to help.