* There's a size limit: Stars need to be massive enough to sustain nuclear fusion in their cores. If they're too small, the gravitational pressure isn't enough to trigger fusion.
* Red dwarfs are the smallest: The smallest stars we know of are called red dwarfs. They are much smaller and cooler than our Sun.
* Brown dwarfs: There's a category of objects called brown dwarfs which are even smaller than red dwarfs. These are sometimes called "failed stars" because they never quite reach the mass needed for fusion. They do, however, emit a faint glow.
So, while there isn't a name specifically for the "smallest star," the red dwarfs are the smallest stars, and the brown dwarfs are even smaller celestial objects.
