A Hairband with Frills. This may be as simple as a ribbon across the top of the head with frills on either side like in post #3040277 or post #3516242. The Fleur De Lapin Uniform notably includes a frilled hairband, and Alice Margatroid wears one as part of her normal costume.
Hairbands with a single upright frill (post #2661396) should be tagged Maid Headdress whether the character is a Maid or not.
A frilled hairband with additional embellishments like embroidery or laces (post #2366937, post #3379468) might be a Lolita Hairband.
