What is the IUPAC nomenclature for the cyclic mono-alkene ions formed after proton or hydride abstraction?
Anions

In general nomenclature, anions may be named by using functional class nomenclature; however, the resulting names are not the preferred IUPAC names. The corresponding subsection of the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) reads as follows:


  P-72.2.1 Functional class nomenclature
  
  Functional class nomenclature can be used, in general nomenclature, to describe anionic compounds. An anion that can be considered as derived formally by adding an electron to a radical may also be named by adding the class name ‘anion’ as a separate word to the name of the substituent group. The names are formed by using the names of corresponding radicals (not necessarily the name of substituent groups) and the class name ‘anion’ as a separate word. The multiplying prefixes ‘di’, ‘tri’, etc., are added to the class name to denote multiple anions. This type of nomenclature is limited to anions having anionic centers in the same structure. Systematic names (see P-72.2.2) are preferred IUPAC names.


The functional class names for the anions that are given in the question are:


cycloprop-2-en-1-yl anion 
cyclobut-2-en-1-yl anion
cyclopent-2-en-1-yl anion
cyclohex-2-en-1-yl anion


The preferred systematic names for anions that can be derived by deprotonation are formed according to P-72.2.2.1:


  P-72.2.2.1 Anions derived from parent hydrides and their derivatives
  
  An anion derived formally by the removal of one or more hydrons from any position of a neutral parent hydride is preferably named by using the suffix ‘-ide’, with elision of the final letter ‘e’ of the parent hydride, if any. Numerical prefixes ‘di’, ‘tri’, etc. are used to denote multiplicity; locants identify positions of the negative charges.


Therefore, the preferred IUPAC names for the anions that are given in the question are:


cycloprop-2-en-1-ide
cyclobut-2-en-1-ide
cyclopent-2-en-1-ide
cyclohex-2-en-1-ide


Cations

In general nomenclature, also cations may be named by using functional class nomenclature; but again, the resulting names are not the preferred IUPAC names.


  P-73.2.1 Functional class names
  
  Cationic compounds that can be considered as being derived formally by removal of electrons from the corresponding radical may be named by adding the class name ‘cation’ as a separate word after the name of the radical. Polycations are indicated by adding the multiplying prefixes ‘di’, ‘tri’, etc., as appropriate, to the class name. Systematic names formed by using the suffix ‘ylium’ are preferred IUPAC names (see P-73.2.2). When the charge is not localized, the structure is enclosed in square brackets.


The functional class names for the cations that are given in the question are:


cycloprop-2-en-1-yl cation
cyclobut-2-en-1-yl cation
cyclopent-2-en-1-yl cation
cyclohex-2-en-1-yl cation


The preferred systematic names for cations that can be derived by removal of a hydride ion are formed according to P-73.2.2.1.2:


  P-73.2.2.1.2 General method
  
  According to the general method, cations formally derived by the removal of one hydride ion, $\ce{H-}$, from any position of a parent hydride are named by adding the suffix ‘-ylium’ to the name of the parent hydride, with elision of the final 'e' in the name of the parent hydride, if present. Di- and polycations formally derived by the removal of two or more hydride ions from the parent hydride are named by using the suffix ‘ylium’ and the multiplying prefixes ‘bis’, ‘tris’, etc. (…)


Therefore, the preferred IUPAC names for the cations that are given in the question are:


cycloprop-2-en-1-ylium
cyclobut-2-en-1-ylium
cyclopent-2-en-1-ylium
cyclohex-2-en-1-ylium