The correct name for the compound OBr2 is ODD bromide or oxygen dibromide.
Dibromine monoxide would have the formula of Br2O.
Probably in ionic compounds where they act as anions. I don't think OBr2 will exist everywhere at all.
OBr2 is polar. It is an angular shape (much like water) and the dipole moment vectors do not cancel each other out. Oxygen will be slightly negative while Bromine would be slightly positive