why isn't this called Riposte or Counter. The description is describing a Riposte or a Counter.

FFG settled on using the terms Improved and Supreme likely is why

What is the benefit?

I fence and while I think it should be riposte rather than parry I don't see it mattering all that much. Thematically and narratively my duel could consist of a whole mess of parrying and riposting. And if I am describing my duel to a fencer I can be pretty descriptive in the process. To be able to use the term Passata-sotto and not have the person need to look it up would be fun.

"Counter" is not a specific fencing term, it could be a counter-attack, counter-riposte, counter-time, counter-parry or a counter-disengagement.

Could also be that they're leaving those names open for future talents that have nothing to do with the Parry talent.

Besides, as Greymere noted, FFG's been using the Improved/Supreme line for talents since EotE. It's worked pretty well, and makes it clear that various talents are an improvement upon the base version.

Before open another post and create some chaos outside, I will use this post if doesn't bothers you

PC A. Attacks with lightsaber
PC B. Uses Improved Parry and "returns" the attack.
PC A. Uses Parry to reduce damage.

This is correct? I supose that PC A cannot use Improved Parry and "return damage" but still can use Parry to protect him/herself?

Thanks!

Before open another post and create some chaos outside, I will use this post if doesn't bothers you

PC A. Attacks with lightsaber

PC B. Uses Improved Parry and "returns" the attack.

PC A. Uses Parry to reduce damage.

This is correct? I supose that PC A cannot use Improved Parry and "return damage" but still can use Parry to protect him/herself?

Thanks!

Correct, because PC B didnt have to roll to hit with improved parry, and so could not get 3 threats or a despair for PC A to activate Improved parry.