The first rule you should know is about selecting between a ring and a chain as parent structure. The current version of Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book) reads as follows:
P-52.2.8 Selection between a ring and a chain as parent hydride
Within the same heteroatom class and for the same number of characteristic groups
cited as the principal characteristic group, a ring is always selected as the parent hydride to construct a preferred IUPAC name. In general nomenclature, a ring or a chain can be the parent hydride (see P-18.104.22.168).
Thus if you only have butene with a phenyl group, the preferred parent structure is the benzene ring and not the butene chain. Therefore, your initial assumption "I initially assumed the name of this compound to be (Z)-1,1-diphenylbut-2-ene as the butene is the main chain, with two phenyl groups attached to it." can generally be ruled out.
In this case, however, another rule is relevant. Since there are two identical parent structures (the two benzene rings), which are not alkanes, multiplicative nomenclature is preferred to substitutive nomenclature.
P-51.3.1 Preferred IUPAC multiplicative names
For a multiplicative name to be categorized as an IUPAC preferred name, certain restrictive conditions must be met. Multiplicative nomenclature is preferred to substitutive nomenclature for generating preferred IUPAC names to express multiple occurrences of identical parent structures, other than alkanes when
(1) the linking bonds (single or multiple) between the central substituent group of the multiplicative group and all subsequent structural units are identical and
(2) the multiplicative groups, other than the central multiplicative group, are symmetrically substituted; and
(3) the locants of all substituent groups on the identical parent structures, including suffix groups, are identical.
Therefore, the preferred IUPAC name for the compound that is given in the question is
Also note that this is not a biphenyl.