By identity info I'm guessing you mean bank accounts, driver's license/passport, even phone numbers? You don't need any of that on any exchange UNLESS you are doing fiat. I personally use bittrex and poloniex for my crypto-to-crypto exchange needs. Bittrex doesn't even care if you use a temporary email (yopmail) to set up an account if you don't even want to use your main email.
Yes, anybody who is planning to do some small trades probably also just testing the water can use wither Bittrex or Poloniex as they are not very strict with verification at that level. I think you have to verify if you want to withdraw fiat money out of their system though I am so sure if that is really the case so talking to the support can clarify things once and for all. I am also into Bittrex because I find it more newbie-friendly compared to other exchanges with confusing interface.