The IUPAC name for the coordination compound [CuCl₂(CH₃NH₂)₂] is

dichlorobis (methylamine) copper (II)

Apologies for the oversight. Let's explain the IUPAC name for the coordination compound [CuCl₂(CH₃NH₂)₂], which is: (2) dichlorobis(methylamine) copper(II)

In the IUPAC name for coordination compounds, we follow a specific format to represent the ligands and the central metal ion.

1. Ligands: Ligands are the molecules or ions that bind to the central metal ion in a coordination compound. In this case, the ligand is CH₃NH₂, which is methylamine.

2. Central Metal Ion: The central metal ion in this coordination compound is copper, and it has a +2 oxidation state, denoted as copper(II).

3. Prefixes and Suffixes:
   - "di-" indicates there are two chloride (Cl^-) ligands coordinated to the central metal ion.
   - "bis" indicates that there are two identical ligands, which is the methylamine ligand.

Putting it all together, the name "dichlorobis(methylamine) copper(II)" indicates that there are two chloride ions and two methylamine ligands coordinated to the copper(II) ion in the coordination complex. The name follows the standard IUPAC nomenclature rules for coordination compounds, making it clear and unambiguous in representing the composition of the complex.