A person becomes a cyborg when they forget that they are human or no longer consider themselves human. In essence, when you forget about your humanity, you suffer machine-like properties and illnesses. You ignore pain and have no conscience for the welfare of anything and become sociopathic. This is called "Cyberpsychosis" whereby having a lot of chrome that is clearly recognizable and alters your "natural" view of the world draws you ever closer to this phenomenon.
An artificial heart would not make you a cyborg as you rarely have to deal with the fact that your heart is cybernetic and not human. Whereas having your arm telescope into a wicked sword alters your perception making you more mechanical.
Most internal cyberware with no DNI has little impact on your humanity, whereas external or exotic body-altering and sense-altering cyber does.
Cyber-vision, Sense-rigs, Skillsofts, implant weapons, cyberlimbs and reaction enhancers have the ability to make you cyberpsychotic. Whereas blood-filters, cyber-organs, muscle replacements and cosmetic ware have little effect (of course, sleeping at night with your inhuman heart never skipping a beat may be unnerving)
The aspect of decorating your chrome is a coping mechanism for the debilitating effect on the user's humanity. It gives you a way to link your cybernetics to your personality, preserving your link to your psyche. Couselling is also an option.
In essence, being a cyborg is based on the threshold which defines you and the machine. A cyborg is a person who is controlled by the machine.
Examples of cyborgs: Robo-Cop and the Street Deacon
Johnny Mnemonic wasn't a cyborg but he was getting there.