I once had an idea for a pokemon-inspired game that took elements from horror games.
Some monsters can be befriended, some can't (much like with taming actual animals), and the game doesn't tell you in advance which are which (with maybe a couple of exceptions in the early game).
There's always an element of uncertainty regarding how much you can trust the monsters that travel with you, but you can't get by entirely without relying on any. How you treat them is also a factor so being too quick to act on distrust may push a loyal monster toward betrayal.
You also have to take into account interactions between monsters because this isn't the kind of game where you can have a prey species and it's natural predator together without taking precautions.
How you go about befriending/taming different kinds of monsters also differs. Some will start hanging around if you feed them (some that are not tamable will also start hanging around if you feed them, like bears). Others may simply find you interesting and hang around to watch if you don't chase them off. Some may have their respect earned by defeating them and then showing mercy.
What monsters you have with you also impacts where you can go and by what method. Pokeballs don't exist in this world. While some monsters can make themselves small for transport, this is not universal.
The "starters," such as they are, are based on three common central elements in horror games: the light, the tool that allows you to access things you otherwise couldn't, and the companion that may or may not prove trustworthy.
These three all have possessed object vibes, and when you choose one, they are presented more like items. I imagine the game doesn't specifically say they are monster companions, and the flavor text describes them like strange objects.
Old Lantern: This would be good to have if you're not back before dark. It seems sturdy and has a comforting weight to it. The flame inside is an odd color. (It kind of looks like it has eyes.)
Ship in a Bottle: The anchor chain can extend and retract, somehow. This might be useful for things that are out of reach. (The details around the bow of the boat almost resemble a face)
Worn Bear: A well-loved beanbag teddy bear. It has been patched with different kinds of cloth. Some of the beans appear to have sprouted. Maybe it will help if things get scary? (Did it just move?)
They start out operating like items. I imagine it almost being a surprise when they start becoming more lively over the course of the first quest (if everyone and their mother weren't familiar enough with Pokémon to have picked up the implications of a choice between something fire-related, something water-related, and something plant-related in a monster taming game).