Both names will be on your paperwork, so here's the whole arrangement before you ask. A company selling certainty shouldn't make you guess about its own structure.
Quality Containers, Inc. is a wholesale container supplier serving cities nationwide, operating since 2014 out of Camarillo, California. They hold the inventory, the grades, the warranties, and the transporter network, and they price at wholesale, without standard retail markup. Boxwright Co. is David Slivinski, your independent sales representative for that inventory: one person who learns your project, finds the right container, and stays reachable from quote through delivery.
What going through me costs you: nothing. Your price is the same whether you call Boxwright or call Quality Containers directly. I'm paid by Quality Containers, not by a markup on your container.