Alexander Waverly, the UNCLE director, explicitly discouraged his agents from getting married. He said that a married agent did not focus on the mission. And that their wives or husbands could be blackmailed by Thrush.
So why the single agent Illya Kuryakin is wearing a wedding ring in the Episode 15? The production crew forgot to hide the ring of actor David McCallum. He was married to Jill Ireland, special guest sate in four episodes: 3, 7, 37 and 87.