Naming ionic compounds of group B
The relevant document including the rules of formal IUPAC nomenclature is the Nomenclature of Inorganic Chemistry — red book from 2005. Section IR-5.4.2.2 (Use of charge and oxidation numbers) is relevant for the cases you discuss. It reads:

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The oxidation number (see Sections IR-4.6.1 and IR-9.1.2.8) of an element is indicated by a Roman numeral placed in parentheses immediately following the name (modified by the ending ‘ate’ if necessary) of the element to which it refers. The oxidation number may be positive, negative or zero (represented by the numeral $0$). An oxidation number is always non-negative unless the minus sign is explicitly used (the positive sign is never used). Non-integral oxidation numbers are not used for nomenclature purposes.
Several conventions are observed for inferring oxidation numbers, the use of which is particularly common in the names of compounds of transition elements. Hydrogen is considered positive (oxidation number $\mathrm I$) in combination with non-metallic elements and negative (oxidation number $\mathrm{-I}$) in combination with metallic elements. Organic groups combined with metal atoms are treated sometimes as anions (for example, a methyl ligand is usually considered to be a methanide ion, $\ce{CH3}$), sometimes as neutral (e.g. carbon monooxide). Bonds between atoms of the same species make no contribution to oxidation number.
Note that oxidation numbers are no longer recommended when naming homopolyatomic ions. This is to avoid ambiguity. Oxidation numbers refer to the individual atoms of the element in question, even if they are appended to a name containing a multiplicative prefix, cf. Example 12 above. To conform to this practice, dimercury($2+$) (see Section IR-5.3.2.3) would have to be named dimercury($\mathrm{I}$); dioxide($2-$) (see Section IR-5.3.3.3) would be dioxide($\mathrm{-I}$); and ions such as pentabismuth($4+$) (see Section IR-5.3.2.3) and dioxide($1-$) (see Section IR-5.3.3.3), with fractional formal oxidation numbers, could not be named at all.

While the section in itself does not mention the possibility of omitting oxidation numbers, the examples obviously do:


$\ce{Na2[Fe(CO)4]}$   sodium tetracarbonylferrate($\mathrm{-II}$), or sodium tetracarbonylferrate($2-$)


The generally accepted rule is that oxidation numbers can be left out if the element in question is commonly known to exist in only one oxidation state. That, for example, includes groups 1 and 2 but also elements such as zinc of which only one state is common.