no need to use the word toupee, wig or system: transplant is also okay, if your system hair is made of natural hair from another human or species

[Fanjeera]

Transplants can be attached in medicine using adhesives. Their name doesn't change due to that: they are still transplant. I've heard men who wear hair say that they only got a transplant, nothing else, and I've considered that lying, but I was wrong. It is correct to call this a transplant. The only difference is that it's not an autotransplant which hair transplant usually is, but an allotransplant which most of the rest of the transplants used in medicine are also and are perfectly well called transplants still.
If you have synthetic hair, though, you could say that you've got an implant.

 

[Regan]

A good point! To call it a "transplant" is no more misleading than to call it a wig. Modern hair systems are quite different from what most people imagine when they think of a wig.

 

[Fanjeera]

if it was artificial, you'd have to call it prosthesis or implant.

 

[Hair2019]

You don't have to tell anyone anything, and there is no reason anyone could know you wear hair if you have the knowledge and ability to make your systems look totally natural. But if you ever choose to talk about it, you could just say you had a hair thickening or enhancement procedure, which is true. I agree you should NEVER use the words 'wig', 'toupee' or 'hairpiece'! Those are outdated and unhelpful terms with negative connotations, and should be erased from your vocabulary.

 

[Fanjeera]

It's a transplant. Just with a different and not so good and strong technique.