Main Question or Discussion Point
Well I have two possible answers, it's either 1-(cyclopent - 1', 4'- dienyl) methyl ethan-1-ol or 1-methyl - 1 - (cyclopent-1',4'-dienyl) ethan-1-ol.
Unfortunately the answer wasn't provided in the textbook.
What is 1-methylethanol?
I would find it simplest to name it 2-(2-hydroxyprop-2-yl)cyclopentadiene, but that doesn't name it as an alcohol so I suspect is not correct.
Note that (i) you must specify the position of substitution on the ring; (ii) the ring is 1,3-cyclpoentadiene, not 1,4. Actually you can just say cyclopentadiene, because there is only one possible cyclopentadiene.
cyclopenta-1,3-dineyl? 1,3? I don't get how you numbered the ring, you have to number the carbon of the ring attached to the main chain as 1'. See diagram. There is no double bond on 3' carbon of the ring.The numbering of the ring atoms is such as gives the lowest numbers to the double bonds (not such as puts the substituent on atom 1). Thus it is cyclopenta-1,3-dienyl and the substituent is on atom 2.