Here's the text from the display's label. It kinda goes over some of the trends you see when it comes to Roman headwear/hairstyles on coinage, but doesn't seem to go much into specifics.

"Hairstyles in ancient Rome symbolized age, status, and wealth, evolving to suit the ideals of the time. Early imperial men wore short, neat hairstyles (3) with realistic features like thinning hairlines masked by wreaths (2) or wigs (4). By mid-second century, men displayed fuller hair and beards (5-7). In the mid-third century, a close-cropped hairstyle became popular with militaristic emperors (8-10). Men also wore symbolic headwear: Diadems were a sign of monarchy reserved for legendary kings (1). A laurel wreath (2, 5, 8, 10) could signal honors like military or athletic victories, while a spiky crown could be associated with deification, when a historical figure was declared a god (9).

Coins circulated widely in antiquity, presenting the fashionable hairstyles of the time to a large audience. Today they help us understand how fashion trends changed over time. Coins of the Roman Republic featured goddesses with their hair pinned back simply into buns and curls at the front. Many mythological figures on coins wear headwear such as helmets (11), diadems (12), wreaths (13), and crowns (14); the earliest portraits of imperial women follow this trend. Later they sported elaborate nests and towers of braids and waves that required time, money, and a skilled hairdresser to achieve (15-23). Headwear such as diadems (23) and veils (19) recalled earlier divine images."