Can we use prefixes like iso, neo, etc in IUPAC nomenclature of organic compounds?
According to the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) various prefixes are retained for use in general nomenclature. However, many prefixes are no longer recommended.


  Trivial, common, and traditional prefixes have always been an integral part of organic nomenclature. However, as systematic nomenclature develops and becomes widely used, many of these prefixes fall by the wayside. Accordingly, each set of IUPAC recommendations contains fewer of these traditional prefixes.


For example, the prefixes “isobutyl”, “isopentyl”, “neopentyl” were contained in the 1993 recommendations but are no longer recommended as approved prefix. The prefix “isopropyl”, is still retained for use in general nomenclature; however, for the preferred IUPAC name (PIN), the preferred prefix is “propan-2-yl”. (The prefix “1-methylethyl” may be used in general nomenclature).

Anyway, the name “5-(1-ethyl-1-isopropyl)nonane”, which is given in the picture in the question, is clearly wrong since no parent structure is given for the substituents 1-ethyl and 1-isopropyl:
“5-(1-ethyl-1-isopropyl what?)nonane”

If you really want to use such a name including the substituents 1-ethyl and 1-isopropyl, the corresponding systematic name would be “5-(1-ethyl-1-isopropylmethyl)nonane”. However, such a name would be highly unusual and not in accordance with the basic principles of IUPAC nomenclature.

The name “5-(1-ethyl-2-methylpropyl)nonane”, which is proposed in the question, describes the correct compound and may be used in general nomenclature. However, the PIN for this compound is “5-(2-methylpentan-3-yl)nonane” since prefixes of the “alkanyl type” are preferred if the free valence is not in position 1 of the substituent group (see this similar question).