Do I set up my rental agreements, or other agreements such as property management, in the name of the Parent Series LLC?

Your rental agreement should be either with a Shell LLC (a traditional LLC set up as an Operating Company) or with the land trust that is housed under your series LLC. The Asset Holding LLC, your Parent Series LLC, should never enter into contracts, lease agreements, etc. Same for property management agreements, except these can also be set up in the name of the land trust as owner of the property. If this is the case, an EIN will need to be obtained for the trust to set up a separate bank account to deposit checks.