I'm wondering are all occupants inhabiting a residency required to be on the lease? What if one person wants sole responsibility of said lease? Is this a landlord/management agency house-rules type situation or are there laws regarding this?

It would depend on the terms of the lease.

First, ANY question on law needs to include your general locale as laws vary by area. This may depend on local laws, but generally, its up to the landlord whether to require all residents sign the lease.