If I was the only person left claiming to be [insert group of people here], would that mean that being a [said group] would be defined by me? Just because there is only one thing claiming to be something doesn't mean you can leave behind actual ancestry.
I (or anyone else) can claim to be a lot of things. That doesn't make it so.
I'd agree with you if we were referring to political parties such as democrats or republicans. Those do (and have) changed over time, likely no longer standing in the same region of the political spectrum as they once did. I'd also agree with you on ambiguous terms like liberal and conservative, which are relative terms. Communism isn't that ambiguous or relative. It represents a fixed set of ideologies like laissez faire[1]. It may not work or it may be completely unattainable, but that isn't the point. If you call something a duck, it should walk like a duck and quack like a duck. If it doesn't, well, it probably isn't a duck.
1. Communism and laissez faire are obviously different ideologically, but they are still somewhat fixed ideologies.
I (or anyone else) can claim to be a lot of things. That doesn't make it so.