Woman (wife): Bianca (ビビンカ)
A little boy (son) and a little girl (daughter) were born at the same time: nobody.
Little killing leopard: Blanco (Bianca will let you choose a name in the game. This is the first name)
According to SFC-DQ5 above.
On PS2 and NDS, the boy's name is Lai Ci Cox (レックス) and the girl's name is Tabassa (タバサ).