Step 1: Find the oxidation number of silver.
In $Na[Ag(CN)_2]$, sodium contributes $+1$ and each cyano ligand contributes $-1$. For the whole formula unit to be neutral: \[ (+1) + x + 2(-1) = 0 \implies x = +1 \]
Step 2: Name the ligands.
Two cyanide ligands are present, which is named dicyano using the standard multiplying prefix di- for two identical simple ligands.
Step 3: Name the metal as part of an anionic complex.
Because the complex ion carries a negative charge overall, the metal's name must end in -ate. Silver takes its name from the Latin argentum, so it becomes argentate, with its oxidation state (I) shown in brackets.
Step 4: Put the cation first and assemble the full name.
The cation sodium is named first, followed by the anionic complex name. \[ \boxed{\text{Sodium dicyanoargentate(I)}} \]