If one has a Form 1 application that has come back as Pending research, will ATF notify (email)when the application is accepted or denied? I used the drop down to give the name of my Rattler and I suspect that is the issue as that name is not engraved on the receiver.

Unless they reject it outright, the next step is that it moves to submitted/in process (the normal initial status for a successfully submission). Then it goes through the normal process and either gets approved or denied.

However, if you put Rattler as the model, and it only says MCX on the receiver, they may reject it. “Rattler” is a SiG branding name for a particular configuration of the MCX, not a model.