It is my understanding that the term 'Reformed Baptist' is of very recent usage. It dates SFAIK from 1963 when Geoff Thomas from Wales and Walter Chantry were at Westminster Seminary, came under pressure to adopt Presbyterian doctrines and declared themselves to be Reformed Baptists. Others say Ernest Reisinger used the term but I haven't been able to find that.
From the 17th Century, Baptists of a Calvinisic persuasion were called Particular Baptists because they believed in particular redemption. Some of them, like William Kiffin, believed in closed communion, while others, like Bunyan, upheld open communion. The former came to be known as 'Strict' or 'Strict and Paticular' Baptists.
I have spent time on the Puritan Board and been told that I'm not Reformed because to be Reformed is to be Presbyterian, but the Presbys didn't patent the word 'Reformed' so knickers to that! I am Reformed and Baptistic, and if anyone doesn't like that - too bad! In fact Reformed Presbys are very thin on the ground in England (different in Scotland), so, while there are some Reformed Episcopalians in the Church of England (think Jim Packer and John Stott), the large majority of Reformed folk in England are Baptists.