Answer is: the name of the unknown oxyanion is hypobromite.
M(NaBrOₓ) = 118.9 g/mol; molecular weight of an ionic compound.
M(Na) = 23 g/mol; atomic weight of sodium.
M(Br) = 79.9 g/mol; atomic weight of bromine.
M(O) = 16 g/mol; atomic weight of oxygen.
M(Na) + M(Br) + M(O) = 23 g/mol + 79.9 g/mol + 16 g/mol.
M(Na) + M(Br) + M(O) = 118.9 g/mol, so compound is NaBrO and oxyanion is BrO⁻.