if you're talking about "Anonymous" exchanges, i'd recommend to use P2P ones, such as Localbitcoins[1] & Paxful[2]. They offer high-privacy trading solutions, but the tradeoff here is that you'll usually pay very high fees.

If you're willing to submit your ID, and have a bank account/VISA that can do SEPA transfers etc, i'd highly recommend you use Coinbase[3], or Bitstamp[4]. You'll pay almost no fees compared to P2P, but then again, you lose all privacy.

[1] https://localbitcoins.com
[2] https://paxful.com
[3] https://www.coinbase.com
[4] https://www.bitstamp.net