The name likely refers to a popular YouTube uploader or a digital promoter from the early era of social media.
Akon and Sean Paul were later added for an official remix to give the song more "riddim" and appeal to the dancehall scene, which was dominating the charts at the time. The "Domenico" Factor
While there isn't a "story" in the sense of a cinematic plot, here is the background on how this specific track came to be: The Origins
It combined the king of R&B (Kelly) with the king of the "lonely" hook (Akon) and the global face of dancehall (Sean Paul).
During the 2000s, specific accounts like "domenico" became go-to sources for curated R&B and Hip-Hop remixes.