If Calvinism wasn't born until the Reformation, then what, using this analogy, would Arminianism be?
No, the gospel has not always had the nickname Calvinism, but the gospel has always been the gospel, given to man in the Garden. I note that God did not tell Adam to go and shed blood and provide an acceptable representative covering for himself (Arminian man centered theology). Even while the man was hiding and blaming his wife, the first tokens of the gospel were presented by God to the man in the form of the covering for his sin (Calvinistic God centered theology). Salvation is of the Lord.
Our theology is at least 6000 years old.
I'll up you one and say that our theology existed before the foundation of the world.
Our theology is Eternal.