No. Absolutely not I'd say - because the purpose of an infrastructure domain isn't obscurity. That is simply a minor side-effect. The #1 reason is to assist in separation of concerns for the control plane, especially given the human factors in managing trust relationships between devices. The name should a) be instantly and recognisably distinct, b) easy and quick to type, and c) not creating risks of fuzzing a trust boundary due to misunderstood hierarchical naming.
Also, no-one should be using AD for SaaS infrastructure. It is a pretty good product for your enterprise internal services, but cannot handle the rather different needs of a SaaS system directory.
Also, no-one should be using AD for SaaS infrastructure. It is a pretty good product for your enterprise internal services, but cannot handle the rather different needs of a SaaS system directory.