Step 1: Identify the ligands.
The complex $[Pt(NH_3)_2Cl_2]$ contains two ammonia ($NH_3$) ligands and two chloride ($Cl^-$) ligands, with platinum as the central metal.
Step 2: Name ligands in alphabetical order.
Ammonia is named 'ammine' (prefix 'di' for two). Chloride is named 'chlorido' (prefix 'di' for two). Alphabetically, 'ammine' (a) comes before 'chlorido' (c), giving 'diamminedichloro'.
Step 3: Determine oxidation state of platinum.
Let oxidation state of Pt be $x$. Charge balance: $x + 2(0) + 2(-1) = 0$, so $x = +2$.
Step 4: Write the full IUPAC name.
Combining: diamminedichloridoplatinum(II). The complex is neutral, confirming the Pt(II) assignment.
\[ \boxed{(B)} \]