Italian name dictionary (Santi e Fanti
T.) includes entries for both of these names.
Isida (or technically Ìsida) is given as a variation of Ìside, which is itself the Italian form of Isis
, the name of the ancient Egyptian goddess. The book says that the use of the name in Italy may have been promoted by the frequent mentions of Ìside in Verdi's opera Aida
Damina is given as the feminine form of Damino, which is said to be a short form of Adamino, which in turn is a diminutive of Adamo
, the Italian form of Adam
. However, the entry goes on to say that Damina can also be from Ippodamia, or from the word dama
, in the sense of "small woman."
P.S. So any way, from these names a Corsican or Italian origin seems more likely than a Belgian one. Neither of the names is listed in the Dutch name dictionary I own.