Could be a variation of Madonna meaning "my lady" in Italian, a name for the Virgin Mary. Maybe Madi from the name Madison, in which the the Mad or Madi part appeas to mean 'Maud' which is a surname. With the popular prefix 'added to create a new name. Perhaps some different form of Madalyn, which is from Madeline, from Magdelene, from Magdalla, a place Galilee. Perhaps teh Mada or as I have seen Madilyn, they Madi was taken and added to 'anna' again. This could very well be a russian variant on any of the above names.