The longest alkyl chain is 5 so it's a pentane.
It has a ketone at carbon 3 so it's a pentan-3-one.
It has double bonds starting at carbon 1 and 4 so it's a pentan-1,4-diene-3-one.
It has 4-methylphenyl substituents at carbons 1 and 5 so it's:
1,5-bis(4-methylphenyl)pentan-1,4-diene-3-one.
If you want to get fancy, and you're sure the stereochemisty of the Double bonds are trans the name would be:
(1E,4E)-1,5-bis(4-methylphenyl)pentan-1,4-diene-3-one