I don't know if this compound exists in real life or not. If it did, what would be the correct IUPAC nomenclature for it? According to me, it could be:
According to this site 1 your second option Cyclohexa-1,3-dien-5-yne is IUPAC acceptable
According to the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book), the preferred IUPAC name (PIN) for the compound that is given in the question is 1,2-didehydrobenzene. The name cyclohexa-1,3-dien-5-yne is acceptable for general nomenclature. The formerly used name benzyne is no longer recommended.