When I have purchased NFA items, the stamps have been issued in the trust name.

However when picking up the items and doing FFL transfer, the 4473 and CBI background were done on a person.

So it seems that the 4473 is separate from trust ownership.

The current pistol brace free registration, say that to register free through a trust, ownership by the trust must be shown to have ownership prior to the publishing date of rule.