Shuyin?

Same place but different time, - He lives in the same city at Tidus (Zanarkand), but the real one, 1000 years in the past
I may seem unfamiliar at first, - Wearing different clothes, strange setting
But reminisce and you'll see
that I'm not that different from before, - Not sure about this one

I love that which has been lost, - Spoiler: He loved Lenne, but then they both got killed.
but through your effort I will gain. - If you beat the game he will be reunited with her.

Who am I? Shuyin.