"I hope she likes it."
Translation:Ελπίζω να της αρέσει.
Yes, there is however a change in meaning: "ελπίζω ότι της αρέσει αυτό" = this refers only to the present, as in she already has it and I hope that she likes it. "Ελπίζω να της αρέσει."= this may also refer to the future, I hope that she will like it once she sees/uses it. The second is a little ambiguous in those terms, because there is no difference in the present and past subjunctive for this verb. Compare "Ελπίζω να το χρησιμοποιεί" vs "Ελπίζω να το χρησιμοποιήσει" (Tenses for αρέσω and χρησιμοποιώ.)
The distinction refers to using the subjunctive (να+verb) instead of πως/ότι. With the subjunctive, you cannot tell for this particular verb what the time point to which we refer is, because both subjunctive tenses are exactly the same. Αυτό is just the object, so it doesn't change the meaning in any way.