I'm fairly certain that the name is "Cyclops". It ends in an "s" so the possessive apostrophe needs to come after the "s", not before.
It's Cyclops' turn now.
It's Cyclops's turn now.
Some people add the possessive "s" after the apostrophe when the name ends in an "s". I don't. I think it looks messy.
Student or Learner