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.