The shotgun is carried over into the Doom 64, mostly untouched. It is first found in the first area of MAP01: Staging Area.
Doom 64's shotgun has a slightly different appearance and a more simplistic cocking sequence (the shotgun only tilts backwards slightly after firing, instead of it being turned vertically and pumped). Observing the weapon's pickup sprite, a barrel band appears to be visible over the forearm, along with a loop beneath the trigger guard. It is possible that it is a lever-action shotgun instead; which would explain the simplified animation, as the action is outside the player's view. This is further supported by its in-game sound effect, which is composed of the exact same two stock SFX as those used for the sawed-off shotgun which Arnold Schwarzenegger makes a famously extensive use of in Terminator 2: Judgement Day. (Do note that their use in Doom predates Doom 64 itself, originating in the PlayStation port.) It's also possible that the reload animation was not included simply due to memory or cartridge space limitations (which is also perhaps the reason why the super shotgun has no reload animation, despite being a single-shot weapon). It's also worth noting however, that Quake has no shotgun reload animation either, thus it becomes very possible that this was merely a stylistic choice by the developers during the Quake era.