Ref: Polo KYC, I just looked at verification and for up to $2000 equivalent/ day, for 'level 1' - all they want is a name and a country.
No verification of name required, no ID requested - so you could even give a false one, it seems.
With your email addy known already - you are effectively traceable to that extent by TPTB anyway.
For most people it's not that scary.
Don't get me wrong, I am concerned about my privacy, but it's not passport and proof of addy until pretty serious amounts - probably way more than you should have on an exchange anyway.
One caution
Poloniex aims to reasonably identify each user by cross-checking user data against governmental watch lists such as OFAC, as well as 3rd party identity verification and authentication services. If a user or a users transaction is flagged as suspicious through our internal controls, Poloniex will require additional proof of identification from the user and has the right to not permit any trades, deposits, and/or withdrawals until additional and verifiable proof of identity is received and the Compliance Officer has approved the user for use of the Platform.
In other words, if you do business there you are at risk of having your coins held ransom for whatever "additional proof" they want, and also possibly the discretion of their Compliance Officer before giving them back.