The Rambo movies are based on the book First Blood by David Morrell that was written in 1972. The first Rambo movie was made in 1982 and was titled the same as the novel. Rambo: First Blood II was made in 1985. Rambo III was made in 1988. Rambo, the fourth film of the franchise, was filmed in 2008.
His dad. (?) R. Rambo, is the name found on a mailbox at the end of the movie Rambo 4. In an earlier scene, Sarah asks Rambo if he had any family. Rambo says that he thinks his father is still alive. R. Rambo is presumably his father.
Currently, there are four films in the Rambo series. They are First Blood (1982), Rambo: First Blood Part II (1985), Rambo III (1988) and Rambo (2008). In 2012, Sylvestor Stallone was in the process of writing a fifth film, but it has since been put on hold.