It's their on business only if it's only visible to themselves. But in a professional field you are expected to dress, groom the part or employers won't hire you. You are very much a representative of the institution when you meet with patients, their families, other clinicians. You aren't on your own time or allowed to do your own thing or express yourself however you want without career implications. This isn't my decision, this dates back to at least the turn of the century. "Dress for success" and looking professional is really not a new concept, but as tattoos/body piercings have become more popular this concept has expanded to relate to those as well. So it's your decision, but a decision with implications on your professional life. That flaming dagger better be worth it.