The IUPAC name of ${\left({\mathrm{CH}}_3\right)}_2{\mathrm{CHCH}}_2\mathrm{Br}$ is:

The IUPAC nomenclature is a method of naming organic compounds based on the compound's structural formula. The carbon in which halogen is attached is taken as the parent carbon atom and numbered that carbon.

As we all know, parent hydrocarbons, functional groups, and lastly substituents are all taken into account when determining an organic compound's name. If a hydrocarbon has just one finally bond, it is said to be saturated. Alkanes is the IUPAC term for saturated hydrocarbons. 
These compounds have names that are determined by their chain-like structure and terminate in "-ane," with the prefix signifying the number of carbon atoms. The number of carbon atoms and the locations of the substituents must first be determined in order to determine the IUPAC name of the given compound.
The IUPAC name of ${\left({\mathrm{CH}}_3\right)}_2{\mathrm{CHCH}}_2\mathrm{Br}$ is 1-bromo-2-methyl propane, it contains the longest chain having three carbon atoms, so propane will be the parent name. and one bromine substituent on the first carbon and the methyl substituent on the second carbon atom.

Hence, the correct answer is option A.