It’s funny, I was at a get together and someone said “oh you have to meet so and so, she is a product designer.” … so we got to talking and I asked where she worked. It was for a financial services company and I said “oh they have a product design group there?” … to which she said “we aren’t real product designers, we just design their app”… it was an isolated instance. Over the past 15 years the titles have shifted in digital design from UX (oh wait, literally everything has UX) to IxD (same problem) to Product Design… maybe in 5 years they will be using something else.
Bottom line, what you call yourself matters little compared to what you can do. That defines you much more. Personally, at this point, I just say designer and if people want to know more they will ask.