Noun no koto literally means "thing of N" and is often used with verbs such as shitte iru (to know), hanasu (talk) and wasureru (to forget). And in your case oboeru (to remember). So it's like "know about Noun", "talk about Noun", "forget about Noun" and in your case "remember about Noun" with Noun being Jona-san (your name?). So he's saying that he remembers about Jona-san. "I remember Jona-san"