notice that on page 31 of that IUPAC link AWK gave us, there are multiple columns for naming polymers under IUPAC.
column 2 = "structural based polymer name"
column 3 = "source based polymer name".
column 4 = "retained original"
column 5 = "no longer acceptable"
notice the additional info.
PIN = Preferred IUPAC Name
bold face = Preferred among source based polymer names
on page 33 column 2 (structural based) you see
on page 33 column 3 (source based) you see
you can see that both those source based names (without other info) apply to all the different variations of the polymer (1,4 & 1,2 & 3,4)
notice the 5 in polyisoprene5. At the end of the table, you'll see this footnote
5 Polybutadiene (polyisoprene) can be used as name for a polymer made from butadiene (isoprene), if the structure is not known.
none of the possible names for your compound have PIN denotation so you can use either
and I would think
would work just as well
As to which you'll find in industry.. "isoprene" has been around for a couple of hundred years now. It's a well known name so much so that if it weren't in the "source based name" (column 3), it would be in the "Retained Original" name, column 4.
and furthermore, if you try to buy (or sell) this chemical, I think you'd have a hard time with poly(1-ethenyl-1-methylethylene).
you choose. all are defendable under IUPAC rules.