I believe the blindness is part of her training.
There's a passage in AFFC:
Without a common language, Arya had no way of talking to the others. She listened to them, though, and repeated the words she heard to herself as she went about her work. Though the youngest acolyte was blind, he had charge of the candles. he would walk the temple in soft slippers, surrounded by the murmurings of the old women who came each day to pray. Even without eyes, he always knew which candles had gone out. "He has the scent to guide him," the kindly man explained, "and the air is warmer where a candle burns." He told Arya to close her eyes and try it for herself.
I'm of the belief that she's blind for a reason and it's all part of the bigger picture, I also believe she'll regain her sight but she needs to learn something and being blind will 'guide' her to that something.
The kindly man also says at some stage
"It would be best if you were blind and deaf as well. You may hear things, but you must let them pass in one ear and out the other. Do not listen."
Whatever Arya is to become, this is just part of the journey. However, having Needle hidden away I think is significant. I hope it means that Cat of the Canals, somewhere, will always be Arya, House of Stark because she is a great little character capable of many things.
Maybe the blindness will help her tune in with Nymeria, it has endless possibilities but unlike TFQ, I hope she regains her sight at some stage in the story.
As for Cat and why she chose that name, I hadn't thought about it before, I thought she chose that name because of all the cats she had seen in Braavos but I could be wrong.
xx