It is very common for a child to be called familiarly by his middle name. All my great aunts and uncles, grandfathers were. I don't have specific confirmation of the two names above belonging to one individual, but if I were researching, I would research under both names and see if they are the same--they could be.
Benjamin Franklin Dodson, was generally known as Frank. But you can find documents under B. F., Ben F., Frank B., and every other permutation you can think of.
Adding at least a few sources will help you assess this. See what the records tell you. As the profile now stands, it is all mythology (history without sources = myth).
Added: I added his son's death record which shows his full name. Lots of other documents for him can be found at FamilySearch.org.