According to the Swedish Historical museum (Historiska museet) the name Arina is known in Sweden since the 13th century. That is about 400 years before Pushkin "invented it".
This is my friend's name. She's from Ukraine but we live in the US. Written down it looks pretty, but its kind of funny to say if you say it like the word arena. I say it more like ear-eena. It's a pretty name, but id suggest using it only if you're of Russian descent. Otherwise it looks kind of a like a "creative" name.