The IUPAC name for the coordination compound \(Na_3[Ag(S_2O_3)_2]\) is

sodium bis (thiosulphato) argentate (I)

The correct answer is (2) sodium bis (thiosulphato) argentate (I).

The IUPAC name for a coordination compound is based on the following rules:

The ligand name is given first, followed by the name of the metal ion.

If the ligand is a polydentate ligand, the prefix "bis", "tris", etc. is used to indicate the number of donor atoms in the ligand.

The oxidation state of the metal ion is given in parentheses after the metal name.

In the case of the complex Na₃[Ag(S₂O₃)₂], the ligand is thiosulphate, which is a bidentate ligand. The oxidation state of silver in the complex is +1. So, the IUPAC name of the complex is sodium bis (thiosulphato) argentate (I).

The other options are incorrect. Option (1), sodium bis (argentothiosulphate) (I), is incorrect because the ligand is not called "argentothiosulphate". Option (3), sodium silver hyposulphate (I), is incorrect because the ligand is not called "hyposulphate". Option (4), sodium silver thiosulphate (I), is incorrect because the ligand name should be preceded by the prefix "bis".