In fact the founders of the company really are called Ben and Jerry. They are Jerry Greenfield and Ben Cohen, and they are old school friends who first met as children in 1963. After leaving school, they both tried various forms of study and work, but without hitting on anything that really worked for them. Finally in 1977 they decided to go into the catering business together - they had various experience by this time, in fact to start with they intended to go into baking and make bagels. However, the initial costs were too high.
They decided to set up an ice cream business in Burlington, Vermont as it didn't have a good ice cream parlour, and Ben Cohen had some experience of the ice cream business. Part of the reason for the rich flavours and chunky textures of Ben and Jerry's ice cream is that Ben has little sense of smell and taste, so was always looking for something that he could enjoy.
The company was an immediate success and was sold to Unilever in 2000.