There are those who argue that “O” in Objectivism should not be capitalized because the word "objectivism" is a noun and not a proper noun. They point out that it is not the norm to capitalize the first letter in words like “socialism,” “communism,” or “fascism.”
The name of a philosophy is capitalized only when the name is coined by modifying the name of the original philosopher—for instance, Platonism, Aristotelianism, Marxism, Leninism, etc. So why capitalize the “O” when the word “Objectivism” is not formed by modifying the letters in Ayn Rand?
Here’s the answer to such arguments:
The reason for which we use capital “O” in Objectivism is primarily philosophical and not grammatical. In the history of philosophy there already exists a “classical objectivism” which is an intrinsicist doctrine. By capitalising the “O” in Objectivism Ayn Rand has clarified that her philosophy is the proper response to the false dichotomy of intrinsicism (classical objectivism) versus subjectivism.
It can be tempting to argue that “Objectivism” is the name of Ayn Rand's philosophy—it is her creation and her brand and therefore it is a proper noun and ought to be capitalized.
But I don't think the idea that the word "Objectivism" becomes a proper noun simply because Rand adopted it can be defended because all the major dictionaries say that the word is a noun. I think it is best to say that "Objectivism" is a proper noun because it stands exclusively for Rand's philosophy which is different from the objectivist doctrines of the past.
Let us consider the word “Selfishness." Ayn Rand has defined Selfishness in a way that is vastly different from the definition in any dictionary. But she has not claimed that her definition has to be accepted simply because she says so. She has made a philosophical case for her stance. She has written books, essays to explain why she defines "selfish" in a particular way. Likewise, we must try to defend the use of capital "O" in Objectivism through a philosophical method.
Journal of Ayn Rand Studies which he edits all the authors are required to capitalize the “O” in Objectivism.