IUPAC name: 1 -Bromo- 4 -chlorobut- 2 -yne.
Rules of IUPAC nomenclature:
i) The longest carbon chain is identified.
ii) The parent chain is numbered so that the multiple bonds have the lowest numbers.
iii) Halogen functional groups are prefixed with the bonding position and take the form fluoro-, chloro-, bromo-, iodo-, etc., depending on the halogen.
iv) Since the double bond is equally distant from either end and the halogen atoms are also equally distant from each end, the carbon attached to a halogen whose name comes first alphabetically would be given lowest numbered carbon in the continuous chain.
v) Triple bonds in hydrocarbons are indicated by replacing the suffix '-ane' with '-yne'.