> I don't want someone branding my arm
That's exactly the point of my analogy?
You're right -- I totally misread what you said. Sorry!
I think tattoo does imply more of a permanence and familiarity in regards to the relationship someone would have with a tattoo on a part of their body they're born with, but I do see your point as well.
When you then have your prosthetic then being an advertisement, it can have an impact on your relationship with the device.
I don't want someone branding my arm and I can see why others would feel the same.