A badge signifies an emblem or insignia of office, an acknowledgement or reward for effort. Dreaming of such an object shows our need to be accepted, not just as ourselves, but also as part of a greater whole.
A brooch also signifies an acknowledgement of value.... Dream Meanings of Versatile
Material aspects: To have our attention drawn to a badge makes us aware of our right to belong to a group.
If a badge is recognizable in a dream we perhaps should try to assess what our feelings are about the organization or group involved. Brooches are often formed of precious or semi-precious gems and can impart a particular message. You might like to consult the entries for gems / jewels, keepsake and jewellery.... Dream Meanings of Versatile