Suppressors are their own entity and are considered a firearm. So in short, they are not registered to a gun unless it’s integrally suppressed. They can be moved between guns at will and provided they are in a trust can be used by anyone listed in the trust. if an individual, then they can only be used under that individuals control. That means no shared access to the storage location.
if a trust is used, each person on the trust has to submit for each submission. Not a big deal, but it slows the process down. Also I believe there is a political reason to slow down trust approvals.