What is the iupac name for the organic compound that reacts with br2?

There are many organic organic compounds which tends to reacts with Br₂. Specifically speaking two classes of organic compounds are very well known for their reaction with Br₂. Those two classes are alkenes and alkynes. Both belongs to unsaturated hydrocarbons. 
This reaction of Unsaturated Hydrocarbons with Br₂ are generally used for the identification of Unsaturation. 

Examples:
                          H₂C=CH₂  +  Br₂   →   Br-CH₂-CH₂-Br

In above reaction Ethene on reaction with Br₂ produces 1,2-Dibromoethane. In this reaction the color of Br₂ (yellow-brown) disappears as the reaction proceeds.

                               HC≡CH  +  2 Br₂   →  Br₂HC-CHBr₂

In this reaction acetylene (alkyne) reacts with two moles of Br₂ to produce 1,1,2,2-Tetrabromoethane.

Hence, every alkene and alkyne for example, Ethene, 1-Butene, 2-Butene 1-Pentene, 2-Pentene, Acetylene, 1-Butyne, 2-Butyne, 1-Pentyne, 2-Pentyne, e.t.c can react with Br₂.