Real Dictionary

badge
Any feature which is regarded as a sign of a particular quality can be referred to as a badge.
countable noun: A badge is a piece of metal or cloth which you wear to show that you belong to an organization or support a cause. American English usually uses button to refer to a small round metal badge.

badge in American English
a distinctive token, emblem, or sign worn to show rank, membership, achievement, etc.
to mark or provide with a badge
noun: a special or distinctive mark, token, or device worn as a sign of allegiance, membership, authority, achievement, etc
transitive verb: to furnish or mark with a badge

badge in British English
noun: a distinguishing emblem or mark worn to signify membership, employment, achievement, etc