I like to do strength training in the evening, but I have a smoothie for breakfast. Is it necessary to drink another smoothie for recovery after a workout, or is one morning smoothie fine?

I'm not dietitian myself, but I think you can refer it based on your feelings, your body after the workout, and also your calories intake per day (if you are controlling your calories), I personally believe that what we eat everyday better based on how our body need.

if your smoothie already contains protein and enough carbs, it's probably enough; otherwise, you could add a quick omelette to go with it or some fruits, depending on if you need proteins or carbs.