He would probably try to investigate the imposter's last known contacts to determine where he might be (easier said than done, he may have to call on a couple brainy friends to help). Once cornered, he'd probably attempt to apprehend them and either turn them into the authorities, or...if they've REALLY abused his reputation for nefarious ends, probably kill them where they stand before they have the chance to do anymore harm, then check his belongings for clues to attempt to fix whatever the imposter's done.