A Remington derringer will be either antique or prohibited. There are basically three different patterns of markings on the top of the barrels. One pattern proves antique status. A second could be antique or not, because production occurred both before 1898 and after 1897. Third variation is definitely modern.
If the pistol is in the proven antique category, you're golden.
If it isn't antique, it is prohibited. You haven't indicated if it is registered or not. At the present time, transfer of registered handguns is frozen.
If it isn't antique, and isn't registered, it cannot be registered.
Do you really want this thread on an open public forum?