It looks really beautiful! I agree with Jeri, probably a hybrid tea but which one is hard to say. There are hundreds of red HTs! In your zone (5 or 6, I'm thinking, I'm near Detroit, Michigan so about the same latitude) you probably won't get another bloom this year before first frost. Depending on the rose, and the weather, I get 2 to 3 flushes of blooms on my hybrid teas each season. Do dead head the spent blooms each time because that does help them to cycle new growth and bloom quicker. However, I'd say keep doing what you're doing because it looks very healthy and happy!
