Open Core is an outgrowth of Open Source because the open-source crowd does not care about freedom, preferring opportunist collaborationism with Big Tech giants (the Big Tech obviously exploits their naiveté for their own gains but what did they expect?). Associating yourself with an open-source movement is associating yourself with this opportunist collaborationism, and I don't know why you would want to do that.

Open Source is synonymous with libre software but not always (as I said before, software that is encumbered with intellectual property issues is not libre, neither is the one tied to non-libre software). While 90% of the time non-libre software is proprietary even if it's made from open-source software (Android), it's not black-and-white, it's more complicated than that.

I'm not saying that "free software" is a better name. It's a terrible name that leads to more confusion, hence "libre software" and "freedom software" are better names.