Currently no - the only way to do that would either be through a Waze Team which I believe is now for all intents and purposes defunct, or through your Wazer Mood Icon, which are just the preset icons and are not fully customizable.

Anyway, icons of drivers are shown very rarely, so this gives no benefit. However you can advertise in any location using https://biz.world.waze.com/

P.S. How did this end up in Latvian forums?