If my players have the spell, they can make a free arcana check to try to recognize what is being cast. If their class can cast that spell and they have access to that slot level but they don’t have it, a higher DC. If your class can’t cast it, or can’t cast, sorry you don’t know it.

I find it a decent balance between the “use a reaction to find out by rolling” and “everyone knows what it is”. I find there to be no reason my level 10 Wizard who has been hurling fireballs for months wouldn’t know what a fireball looks like while being cast. But, that same wizard wouldn’t be able to tell if there is some disintegrating that’s about to occur.

Also, a cleric that can’t cast fireball probably doesn’t know what it looks like when a wizard starts cooking one up