It’s named a French Roll. My Mother in law is french. All the images I’ve seen of her in her younger years, she had this perfectly groomed hairstyle. It’s timeless and looks as “chic” today as it did 40 years ago.I find it perfect for all ages as you can see from the images it depends on how you approach doing it.
Modern French roll hair
To make it look modern and trendy, I suggest setting a good base in the hair and basically rolling it up and coiffing with your fingers to keep it raw looking. For a more classy or grown up approach, use a proper styling brush.
The recipe below is pretty straight forward. Do a little back combing on the crown first to give volume or attitude and then follow the diagram by pinning a line of bobby pins up the centre back of the head then taking the heavy side and rolling the hair into a tight roll and secure invisibly by threading U shaped hair slides up through the outer side.