IUPAC name of $\mathrm{N}{\mathrm{a}}_3\left[\mathrm{Co}{\left({\mathrm{NO}}_2\right)}_6\right]$ is:

Sodium is the counter ion that consists of cobalt (III), so we write complex ion. and also contain 6 $N{O}_2$ groups, so, it will be hexa nitrite. We get hexanitrocobaltate(III)  which is a negative ion, combining we get the name of the compound as sodium hexanitrocobaltate(III).

The following is a list of some IUPAC-recommended guidelines for the nomenclature of coordination compounds. If both the cation and anion names are provided, we would write the cation's name first, followed by the anion's name.
The core metal is listed first, then the names of the ligands in alphabetical order. The name of the centre metal is followed by the Roman numerals indicating its oxidation state. Now, the name of the central metal remains the same whether the complex ion is positively charged or neutral, but if it is negatively charged, we add the suffix "-ate" to the name of the central metal.
Finally, we have a few more regulations regarding the name of ligands:
Most of the time, we refer to neutral ligands by their common names, but there are a few exceptions, like NH₃-ammine, NO-nitrosyl, CO-carbonyl, and H₂O-aqua
The name of an anionic ligand ends in "-o."
Greek prefixes, such as "di- or tri-," are used to indicate the number of ligands present. However, if the ligand's name already has a Greek prefix, alternate prefixes are used instead, such as "bis- or tris-," and their names are placed in parentheses.
When determining the alphabetical order, the prefixes are omitted.
Here, in $\mathrm{N}{\mathrm{a}}_3\left[\mathrm{Co}{\left({\mathrm{NO}}_2\right)}_6\right]$, the anion is a complex ion and the cations are sodium ions. The name would therefore begin with "Sodium." Now that there is just one kind of ligand linked to cobalt, the alphabetical order doesn't matter. Since there are six "nitro" ligands present, we will use the prefix "hexa-" in accordance. Since the complex ion is an anion, cobaltate will be the main metal. "Sodium hexanitrocobaltate" is now available.
According to the charge neutrality principle, we must now determine the oxidation state of cobalt as follows:
${\mathrm{Na}}_3\left[\mathrm{Co}{\left({\mathrm{NO}}_2\right)}_6\right]=0$
$[3\times (+1)]+\mathrm{Co}+[6\times (-1\left)\right]=0$
$+3+\mathrm{Co}-6=0$
$\mathrm{Co}=+3$
Therefore, finally, the name would be written as Sodium hexanitrocobaltate (III).

Hence, the correct answer is option B.