Naming a molecule with both alcohol and aldehyde functional groups
You have correctly identified the principal characteristic group as well as the principal chain. Thus, the parent structure of the compound is pent-2-enal. You also correctly included the ‘3-methyl’ substituent.

The missing $\ce{-OH}$ group cannot be expressed as suffix ‘ol’ since it is neither the principal characteristic group nor situated on the principal chain. Therefore, it has to be indicated by the prefix ‘hydroxy’. The corresponding rule in the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) reads as follows.


  P-63.1.4 Substitutive nomenclature, prefix mode
  
  Hydroxy groups are indicated by the prefix ‘hydroxy’ when:
  
  (1) a group having priority for citation as the principal characteristic group is present; or
  
  (2) a hydroxy group cannot be denoted by a suffix.


In this case, the hydroxy group is placed on a methyl side chain, which results in the compound substituent group ‘hydroxymethyl’.


  P-29.4 COMPOUND SUBSTITUENT GROUPS
  
  P-29.4.1 Compound substituted substituent groups
  
  A compound substituted substituent group is formed by substituting one or more simple substituents into another simple substituent that is considered as the principal chain. The choice of the principal chain is fully discussed in Section P-44.3. The first criterion to be applied is that the principal chain is the longest chain; it will be applied in the following examples of acyclic compound substituent groups.
  
  (…)


Parentheses are used around such compound prefixes in order to avoid ambiguity.


  P-16.5.1 Parentheses (also called curves or round brackets)
  
  P-16.5.1.1 Parentheses are used around compound (see P-29.1.2) and complex (see P-29.1.3) prefixes; after the multiplicative prefixes ‘bis’, ‘tris’, etc.; to enclose a multiplied parent compound consisting of a parent hydride and a substituent suffix or a multiplied substituent prefix even though preceded by a basic numerical prefix, such as ‘di’, ‘tri’, etc.


Therefore, the complete systematic name for the compound that is given in the question is (2⁠Z)-2-(hydroxymethyl)-3-methylpent-2-enal. (Also note the stereodiscriptor for the double bond.)