Answer
Name of the compound $B_{2}Cl_{2}$ is diboron dichloride.
Work Step by Step
$B_{2}Cl_{2}$ is a molecular compound made of 2 non-metals. From fig. 3.10, we see that they are named as: $prefix + name \hspace{1mm}of \hspace{1mm}1^{st}\hspace{1mm} element \hspace{1mm}+\hspace{1mm}prefix+\hspace{1mm}basename\hspace{1mm}of\hspace{1mm}2^{nd}\hspace{1mm}element\hspace{1mm}+\hspace{1mm}ide $
Base name of chlorine is $-chlor$. Also, prefix is $-di$ for both elements. So, name of the compound $B_{2}Cl_{2}$ is diboron dichloride.