This is probably going to result in me embarrassing myself, but isn't 'eponymous' mean something along the name of 'bearing the same name'?

Like 'the film JFK focuses not on its eponymous President, but on the conspiracy theories surrounding the shooting' Or 'Russell Crowe plays the eponymous hero in Robin Hood/Gladiator'.

So, no the sentence wouldn't make sense - the film would have to be called Chekov, wouldn't it, for it to make sense?

I was tempted to look it up and check but haven't. I might once I've submitted this though!