Does the name 4-nitrodiphenylmethane follow the IUPAC rules?
The preferred IUPAC name for the compound that is given in the question is 1-benzyl-4-nitrobenzene; however, that does not necessarily mean that other names are not in accordance with IUPAC nomenclature.

The name diphenylmethane actually is in accordance with current IUPAC recommendations (see Subsection P-44.1.2.2 in Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book)), although the preferred name is 1,1'-methylenedibenzene (see also this answer).

The name diphenylmethane treats the phenyl groups alike as substituents of methane.

If now one of the simple phenyl substituents in diphenylmethane is replaced by a compound 4-nitrophenyl substituent, the analogous name of the resulting compound is (4-nitrophenyl)(phenyl)methane and not ‘4-nitrodiphenylmethane’.