You have two choices for choosing the parent hydride here in this case.
1. Choosing the cyclohexene ring as the parent hydride
If we consider the cyclohexene ring as the parent hydride, we get the cyclopentadiene ring to be a substituent leading the name to become 1-(cyclopenta-1,3-dien-1-yl)cyclohex-1-ene
2. Choosing the cyclopentadiene as the parent hydride
If we choose the cyclopentadiene as the parent hydride, the cyclohexene ring becomes the substituent and we get the name of the compound to be 1-(cyclohex-1-en-1-yl)cyclopenta-1,3-diene
Now, what do we choose - the cyclopentadiene or the cyclohexene?
The preferred IUPAC naming
According to P-44.2.1 of the Nomenclature of Organic Chemistry – IUPAC Recommendations and Preferred Names 2013 (Blue Book), we gain the rules to determine seniority in ring systems.
P-44.2.1 The senior ring or ring system:
(a) is a heterocycle;
(b) has at least one nitrogen atom;
(c) has at least one heteroatom (in the absence of nitrogen) that occurs earlier in the following sequence:
F > Cl > Br > I > O > S > Se > Te > P > As > Sb > Bi > Si > Ge > Sn > Pb > B > Al > Ga > In > Tl;
(d) has the greater number of rings;
(e) has the greater number of skeletal atoms;
(f) has the greater number of heteroatoms of any kind;
(g) has the greater number of heteroatoms occurring earlier in the sequence:
F > Cl > Br > I > O > S > Se > Te > N > P > As > Sb > Bi > Si > Ge > Sn > Pb > B > Al > Ga > In > Tl.
Therefore, via P-44.2.1 (e), we have the cyclohexene ring as the the main parent hydride. Therefore, the name found in choice 1 is the PIN of the compound. Thus, the PIN of the compound becomes 1-(cyclopenta-1,3-dien-1-yl)cyclohex-1-ene
