Although pets have been an integral part of the Fallout world ever since the first game (with Dogmeat the dog) in the series, there is no real system for this in Fallout 76. Now, however, it seems to be on the way, as noted by data miners on the Fallout 76 Datamining Discord (via Windows Central).
Back in 2021, Bethesda announced that it intends to add pets to the game, but the feature has since been glaringly absent. One can suspect that the boost for the game after the acclaimed TV series has strongly contributed to Bethesda prioritising popular and requested features like this, and the data miners have found images and icons that clearly indicate that there seems to be several kinds of pets you will be able to choose from.
There is also an early tutorial available, which suggests that it will be a deeper system where your pet(s) will have a more involved function than just being a charming gimmick.
We’ll get back to you when we know more.