When we speak of free will it is good to discern between two separate ideas:
1) Free will independent of physical world. (commonly referred to as libertarian freewill)
2) Human choice and decision making.
Both compatibilists and determinists agree the first of these does not exist and the second one does.
However, they disagree on the definition of the word “free will”. Determinists believe the term “free will” refers to the first phenomena: action independent of the physical world. Compatibilists believe the term “free will” refers to the 2nd phenomena: human choice and decision making.
I believe the term has traditionally referred to the first of these phenomena, for why else would the debate between determinism and free will even exist? No one would claim humans do not make decisions (our brains evolved specifically to make increasingly better decisions). The insight of determinism is that the choices and decisions we make are ultimately determined, hence the term determinism.
Thus, I feel the term compatibilism is misleading. It suggests they’ve made some great insight that the traditional notion of free will (libertarian freewill) is compatible with determinism. it is not.
That said, a good case can be made that the term “free will” is better defined as our capacity to make decisions. In fact, this use of the word is more congruent with common speech (we say we have free will all the time). But if compatibilists wish to adopt that definition, they ought to call themselves revisionists not compatibalists as they have simply revised the traditional definition of free will in this debate to be compatible with determinism.