When it comes to exchanges, there are two types:

• Centralized exchanges (CEX)
• Decentralized exchanges (DEX)

Centralized exchanges are easier to use, they have a bigger userbase, and more liquidity. But what you gain in simplicity and user convenience, you lose in privacy and hefty service fees. Most CEX-es require that you complete KYC before you can withdraw. 
Take a look at https://coinmarketcap.com/rankings/exchanges/ for list of the most popular CEX-es.

DEX's are less popular but in sync with bitcoin's main ideas. You are not handing over control of your assets and there is no need for KYC. Bisq is a popular and often recommended DEX.
For other names, you can look here > https://coinmarketcap.com/rankings/exchanges/dex/.