I feel like I knew what this thing was right up until I had one. Two tool id site had no idea, and one said it's a ball joint separator, but I can't find any that look like this, and I swear I've seen them in stores, but can't remember where.
Maybe a type of bearing press?
It depends on what the puller is intended for. Tie rod end/pitman arm pullers and u-joint pullers often have fixed jaws. OP didn't include anything in their picture to indicate size, but the tool in their picture looks almost exactly like an old tie rod puller my dad had from the 70s or 80s.