IUPAC Naming of CH3C(p-ClC6H4)2CH(Br)CH3
According to the current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book), a structure with two or more identical units that are linked by di- or polyvalent groups can be named in two ways:

by ordinary substitutive nomenclature, in which one of the parent structures is chosen as the senior parent structure and the remainder of the structure is expressed by substituent prefixes
by multiplicative nomenclature, in which two or more parent structures are connected by symmetrical or unsymmetrical single or concatenated substituent groups

Both methods yield correct names, which may be used in general nomenclature. However, the IUPAC recommendations define a preferred IUPAC name (PIN), which is the name preferred among two or more names generated from two or more IUPAC recommendations.
For the compound that is given in the question, the preferred IUPAC name is actually generated using multiplicative nomenclature (see also What is the rationale of the IUPAC name for DDT?), which yields the name 1,1'-(3-bromobutane-2,2-diyl)bis(4-chlorobenzene).
In general nomenclature, nevertheless, you may choose the butane chain as the senior parent structure and generate the complete name using substitutive nomenclature.
The most important criteria for the numbering in substitutive nomenclature according to the current version of the IUPAC Recommendations are:

P-14.4 NUMBERING
When several structural features appear in cyclic and acyclic compounds, low locants are assigned to them in the following decreasing order of seniority:
(…)
(c) principal characteristic groups and free valences (suffixes);
(…)
(e) saturation/unsaturation:
  (i) low locants are given to hydro/dehydro prefixes (…) and ‘ene’ and ‘yne’ endings;
  (ii) low locants are given first to multiple bonds as a set and then to double bonds (…);
(f) detachable alphabetized prefixes, all considered together in a series of increasing numerical order;
(g) lowest locants for the substituent cited first as a prefix in the name;
(…)

Since the compound that is given in the question has no principal characteristic group and the butane chain, which is taken as the parent structure, has no multiple bonds, the rules (c) and (e) are not relevant in this case.
Thus, all substituents are considered together according to rule (f). Therefore, the correct name is 3-bromo-2,2-bis(4-chlorophenyl)butane and not 2-bromo-3,3-bis(4-chlorophenyl)butane since the locant set ‘2,2,3’ is lower than ‘2,3,3’.