There are several synonyms for the word "hat ring", which is a circular impression left on the hair by wearing a hat. Some of these synonyms include "hat line", "hat band", "hat mark", and "hat indent". These terms are used to describe the same phenomenon when someone has been wearing a hat for an extended period. The hat may leave a noticeable impression on the hairline, which can be a sign of style, but can also be a nuisance if it remains for a long time. It's essential to note that these terms are interchangeable and can be used in place of "hat ring" depending on personal preference and the context in which they are used.