I don't understand this... Why will an exchange ask for an ID before users can trade? I don't know because I don't use Kraken. Exchanges like Yobit, C-cex and bittrex which I use don't ask for any ID. OP can make a switch. Don't let Kraken limit you!
they deal with fiat so they're bound to all the money laundering stuff that requires id. alt only exchanges are creeping towards that too.
But then, It's just isn't right. I thought Bitcoin should be about everything anonymous. Why the need to submit personnel details? I suggest OP finds other exchanges that allow Trading without requiring
personal details.
If you are looking for the most amount of anonymity, use a peer-to-peer exchange, like Paxful or localbitcoins. Or look for other traders like on here or on online classified sites like Craig's List or Back Page. Most in-person traders do not ask for any id.