This Unnamed Man is a soldier in the Barese crew, and a member of the DiMeo crime family.
He attended Melissa Barese’s wedding along with his Wife and Daughter. When Larry Barese told the other Mobsters at the wedding about the incoming indictments being brought onto the family, they decided to gather their families and go home so they could get rid of incriminating evidence. The man went to get his wife and daughter, but his wife took the large flower vase before they left. (The Legend of Tennessee Moltisanti)