How do you name an alkene using IUPAC rules if the longest carbon chain in this alkene does not include the double bond?
The IUPAC recommendations on this matter have been changed. In the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book), the order of seniority between unsaturation and length of chain given in earlier recommendations is reversed:


  (…), the first criterion to be considered in choosing a preferred parent acyclic chain is the length of the chain; unsaturation is now the second criterion.


For example, a preferred IUPAC name is 3-methylidenehexane (not 2-ethylpent-1-ene) since the longer chain now supersedes a shorter unsaturated chain. (This example is given in the Blue Book.)



Besides, the prefix ‘methylene’ is no longer recommended in IUPAC nomenclature to designate the $\ce{=CH2}$ group. The preferred prefix is ‘methylidene’.

Therefore, the correct name for your example is 2-bromo-4-methylidenehexane.