WordNet records no synonym and no antonym for badge. It is the only member of each of its synsets, which is common for technical, taxonomic and single-sense vocabulary — there is no other English word that means the same thing. The broader and narrower terms below are the useful relations in that case.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
an emblem (a small piece of plastic or cloth or metal) that signifies your status (rank or membership or affiliation etc.)
“they checked everyone's badge before letting them in”
Synonyms, antonyms and the broader and narrower relations for badge come from Princeton University’s WordNet. Full sources and licences.
any feature that is regarded as a sign of status (a particular power or quality or rank)
“wearing a tie was regarded as a badge of respectability”
put a badge on
“The workers here must be badged”