well, that's not an easy one. I guess it's literary language. "Прозванья" means "a nickname", and "топни ножкой" means "to stamp (one's foot)", which in this context means "to be displeased, to be capricious"

or, to be more precise, "to act capricious, to show your displeasure with smth"

like to pout?

maybe like a crybaby?

yeah, pout

Thank you!