When someone tries to sound overly fancy with their vocabulary, and does not want to use the proper word, "suffix", they may use this term d'art. In this case, the person is creating a variation to "suffix" by using the prefix "post-" (as in "post-war" for "after the war", or "post malone" for "after the era of Karl Malone"
"As the third generation with his name, Greg G wanted to add a suffix such as 'the third/III' to his name. To try to impress the judge, he suggested that a 'postfix' should be added to his name, much to the chagrin of the courtroom"