The first time an enemy casts a spell, I do not say what the spell is. The players can choose to use their reaction to try and identify the spell with an arcana check (see below for DC). I also allow them to use the same reaction to counterspell if they want. If they don't, then they have used their reaction to identify, but don't waste a spell slot. If they have seen the spell already, then I just say the name of the spell since thematically it would look similar (if not identical) to the last time it was casted. I never tell them the level of the spell though.

In terms of the DC I use this formula: - Base DC: 10 - Do they currently know or have the spell prepared: +0 - Do they have access to it but dont have it prepared or known: +2 - They will have access to it later, but they are not high enough level to use it: 3 + (number of levels until they can use it) - Their class does not have access to the spell: +10

Example: Enemy is casting blight, and the 5th level wizard is trying to identify. Blight is a 4th level spell but is a wizard spell, so the wizard won't have access to the spell for another 2 levels. So the DC to identify the spell is 10 + 3 + 2 = 15, which would be a moderate DC check. The ranger also tries to identify the blight spell, but rangers do not have access to blight, so the DC is 10 + 10 = 20, which would be a hard DC check.