Labels began to appear in women's clothing with the rise of the couture house system in Paris. These were woven into the internal waistband (Emile Pingat example), mainly at the center back, but sometimes on the sides. Fairly soon after their introduction, these started to appear on the wares of more ordinary dressmakers - expensive dressmakers, but ones operating on a more local scale than couturiers in Paris with boutiques in multiple cities across the globe - and high-end department stores.
The hanging tag (the sort you see today) started to appear in the early twentieth century, with the rise of the cheap ready-to-wear industry. More upscale RTW clothing featured a label that was sewn to the garment on two or four edges. The label or tag could be put in various places on the garment (behind the neck, in a side seam, etc.); by the 1960s, the back of the neck had become the standard placement.