Hence the compound above is rightly named as 3-pentene-2-ol ? However, I was wondering whether I can name it as 2-hydroxypent-2-ene ??
Generally, since many compounds can have two or more names in accordance with several methods recommended by IUPAC, a compound may be named correctly in more ways than one. Therefore, the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) include the definition of a preferred IUPAC name (PIN), which is the name preferred among two or more names generated from two or more IUPAC recommendations including the many retained names.
The PIN for the compound that is given in the question is (3E)-pent-3-en-2-ol.
Other names that are in accordance current IUPAC recommendations and also many names that were generated according to earlier recommendations may be used in general nomenclature.
Furthermore, the IUPAC nomenclature is quite robust. In many cases, wrong names (e.g. deviations from the rules for the priority of suffixes, numbering of locants, or order of citation in the name) do not necessarily lead to wrong structures.
The first name 3-pentene-2-ol that is proposed in the question is not in accordance with current IUPAC recommendations. However, the very similar name 3-penten-2-ol (note the elision of the ‘e’) was in accordance with the obsolete 1979 IUPAC recommendations. Hence, the proposed name could be understood.
The alternative name 2-hydroxypent-2-ene that is proposed in the question is not in accordance with current or past IUPAC recommendations; therefore, it should not be used. Nevertheless, this name is unambiguous; it describes only one compound (ignoring cis/trans isomerism). Hence, this nonconforming name could still be understood. The correct name for this compound is pent-2-en-2-ol (the following structure diagram shows the 2Z isomer).
Anyway, the proposed name 2-hydroxypent-2-ene as well as the conforming name pent-2-en-2-ol do not describe the structure that is shown in the question (note the position of the double bond). Therefore, the proposed name cannot be used.