In 1736, Ben Franklin helped establish the Union Fire Company, the first fire department in Philadelphia. After witnessing the more efficient, albeit loosely organized, fire fighting organization in Boston, Franklin sought to make improvements in fire fighting in Philadelphia. The formation of the Union Fire Company was encouraged by others and Franklin published a number of articles in the Pennsylvania Gazette stating the need for more efficient fire prevention.
In Fahrenheit 451, prompted by his conversations with Clarisse, Montag becomes bold enough to ask Beatty if firemen used to prevent fires rather than start them. Stoneman and Black find the idea ridiculous and this is when they bring out their notebooks to state their version of history:
Established, 1790, to burn English-influenced books in the Colonies. First Fireman: Benjamin Franklin.
As with other aspects of society in Fahrenheit 451, history has been rewritten to accommodate the dominant ideology and way of life; the most obvious fact changed is that firemen started fires rather than prevented them. Also, Franklin was not the first fireman; he was part of the push to form the first fire department in Philadelphia. (The first full-fledged volunteer fireman was Isaac Paschall.) And of course, fire departments were not formed, initially, to create fires, let alone create fires to burn English-influenced books. Those responsible for rewriting this part of American history chose to suggest that "fire departments that started fires" were established to burn books with English or British influence; this would have coincided with the aftermath of the Revolutionary War. Thus, in this version of history, the first firemen burned British-influenced books to further separate the United States from England, just after the United States had won their independence from England.
So, clearly all of the histories of the Firemen of America in Fahrenheit 451 are distorted or just rewritten. Why continue to use Franklin as the founder? This was useful because in keeping some ties to history, the new version would seem more believable. In other words, if Beatty and the authorities in Montag's society really want to rewrite history, they would have to do so slowly so that it would not arouse suspicion. Ben Franklin is/was such a huge part of early American history (and the early history of fire departments) that he could not be eliminated altogether. So, they keep Franklin a part of that history but they just change some of the details. Over time, they change more details until it eventually becomes quite different or nearly the opposite of that original history.
It is also fitting that they chose 1790 as the beginning of their version of the history of firemen because this was the year Franklin died. It's as if this marked the end of the real history of fire departments and the beginning of the rewritten history.