To actively pursue memorizing note names and try to associate them with certain keys is too specific, too end game – too specialized an approach. Rather, we could try a different approach. How about we observe the relationship between notes, hear what it SOUNDs like, notice what it FEELs like).
In fact, if you don’t “know” the intervals you are probably going to have a hard time playing that area of the music. That’s why those people who “play by ear” never need to look at notes on paper. We work on feeling, seeing and hearing the relationship of notes. You’ll see how it works after a couple of lessons, and I think you will like it!