A person who specializes in cybernetics is a cyberneticist, or perhaps more formally a doctor of cybernetics if they're educated and licensed. Though if you were dealing with an unlicensed surgeon who wants to be called doctor anyway, it may be in your best interest to humor them rather than antagonize the person sticking machinery in your body.
Someone who installs cybernetics is called a "surgeon", as it is a surgical procedure to install a prosthetic - just a very advanced prosthetic. For example, you would go to a surgeon tomorrow if you were getting a pacemaker installed.
Someone who makes cybernetics is called an "engineer". Engineers do specialize in the real world - the subfield is called biomedical engineering, for engineers who make prosthetics. Typically, one of the engineer's jobs when designing the prosthetic is ensuring that the surgeon can readily install it - it is an explicit design goal that surgeons be readily capable of installing them.
Engineers do specialize in the real world...
Surgeons specialize in the real world too; you probably wouldn't get the same surgeon next year for your hip replacement that you had last year for your LASIK.
That being said, I agree with other above posters that "cyberdoc" is probably what the common shorthand would be for a person who is professionally employed as a surgeon who specializes in cybernetic procedures. We use phrases like, "my eye doctor said such&such" or, "I got a prescription from my ENT."
What about some cool call sign, titles or handles that a Cyberneticist would have? Dr. Hook, Dr. Gunnar Armstrong, Mr. Plug and Play, The Full Metal Cyberneticist, Lead Foot, etc.
The Barber (in ye olden tymes your barber did surgery as well as cut your hair).
Candlestick (a joke, from "a butcher, a baker, and a candlestick maker"... clearly they're actually a butcher).