What would Calvin have thought of ‘Calvinists’?

Probably not much. He attacks the idea of factions in the church being called by a leader’s name when he writes about monasticism:

And that there might be no doubt as to their separation, they have given themselves the various names of factions. They have not been ashamed to glory in that which Paul so execrates, that he is unable to express his detestation too strongly. Unless, indeed, we suppose that Christ was not divided by the Corinthians, when one teacher set himself above another; and that now no injury is done to Christ when, instead of Christians, we hear some called Benedictines, others Franciscans, others Dominicans, and so called, that while they affect to be distinguished from the common body of Christians, they proudly substitute these names for a religious profession.