badge
noun

1 (BrE) a small piece of metal, fabric or plastic, with a design or words on it, that a person wears to show that they belong to an organization, support sth, have achieved sth, have a particular rank, etc:
the school badge She wore a badge saying 'Vote for Coates'. All employees have to wear name badges.
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2 a small piece of metal that you carry or wear to prove who you are, used, for example, by police officers:
He pulled out a badge and said he was a cop.

3 (written) something that shows that a particular quality is present:
His gun was a badge of power for him.
4 (especially AmE)     PATCH