Where does the word Hinduism come from?
It comes from Hindu, which was the Persian exonym for the सिन्धु river.
So is that it? Should we call ourselves *sin[dh]u [dh]armI(o)* now if we want to use pure language?
Well, even "sin[dh]u [dh]arma" is not attested in many places in our scriptures. Also, Sindhi is now seen as a word to refer to those from the specific region of the Sindhu river. Few places mention the phrase "sanAtan [dh]arma", so many have started calling themselves this as well, but this is an obvious attempt to sidestep the fact that the alternative word is an exonym.
Many so-called Hindus make certain claims about the body of Vedic-Puranic (and others in that traditon) texts which are patently false and perpetrated by the westoid scum like Max Mueller in an attempt to subvert the Aryan people. These include, but are not limited to:
>We worship 330 million Gods!
<Actually, we do not worship 33 Crore deities, the word koTI as it was used in the reference you are going to give me could have also meant "traits" or "qualities", which sounds a lot more reasonable. The deities themselves are also usually the personfications of such traits. Vishnu's avatars have usually represented some aspect of strength, Bramha's, some aspect of wisdom, and Shiva's, some aspect of patientce or rational thinking.
>We used to have a discriminatory caste system, but we're past that now!
<There was no caste system inherent in the Dharmas of Aryvarta, whether Vedic, Jain, or many other Dharmas which were unable to survive 1,300 years (and counting) of maximum-overdrive subversion. The closest thing to the modern caste system in that time was a method of social stratification and personal judgement called "Varna", which would be able to tell you what to do with your life given that you factor in the professions of your family members, any and all familial or community traditions, your current profession, etc.
<If both my parents and all my uncles and aunts were teachers, for instance, I would be silly to pass up that opportunity and at least learn to teach so as to have it under my belt, if not to actually make a career out of it. Even if I was planning to go into another, but still sagely profession, I would do well to gleam from my family the general ways of sagehood
<Read https://varadforfreedom.wordpress.com/2020/08/27/defense-caste-system/
>etc. etc.
A lot of these claims you instinctively realize there is something wrong with. Why not the same with the ridiculous claim that the Aryans all believed one set of things dictated by one body of scripture?
Family tradition > Village/community tradition > Kingdom tradition > Pan-Aryan tradition (such as it is)