Many people on the right say "we are Capitalists". Either they don't know that the word Capitalism is a pejorative invented by Karl Marx or else they know this but use the word anyway as an appropriate badge, whatever its source. In fact they may see it as a badge of honour: The epithet given by an enemy.
The problem is, "Capitalism" is not even an appropriate word for describing what we on the right support. In this, as in most things, Marx got it wrong.
What is the appropriate word, then? What word should we on the right use?
There isn't one.
And that's the way it should be.
There isn't a word, and we don't have a system to apply a word to, anyway.
The only theoretically appropriate word would be something uselessly generic, such as "reality". "We support reality"? meh
The left needs a word and a system because they are creating an alternate reality; an invented system with an invented type of people ("Soviet Man") populating it, and so it is meaningful and useful to give their system a label and a definition. We call their system Socialism and we can get a functioning definition of it from any good dictionary.
However, we on the right are not opposing "our" system to their system. It's not a "Battle of the Brands", or "Coke versus Pepsi". We don't have a system to oppose to the left's. The left are battling reality all by their selves. We are on the sidelines; we're dad watching junior trying to hammer a square peg into a round hole. The main thing is to keep junior away from sharp objects, until he learns better.
PS. The titles of two of the most important books by the great Austrian economist, Ludwig von Mises, illustrate the point: One is called Human Action and is descriptive of natural economic activity, the other is called Socialism and defines, describes and draws out the implications of that invented system.
Von Mises was the economist who, in the beginning of the 20th century, proved mathematically that socialism would not and could not work (because there is no way for a socialist system to determine efficient prices). Many prominent economists spent fruitless years trying to find a flaw in von Mises' argument, while at the same time ignoring the devastating reality in the new Soviet states that was playing out in front of their noses, and incidentally proving von Mises correct. But then, ignoring/replacing reality is the point of inventing a system.