Anonymity: You do not need to provide personal information to make an exchange. You don't even need to register.
You forgot to mention there's a big but:
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AML / KYC-
Terms of Use-
Privacy PolicyRule of thumb (my personal observation):
if you see Monero on some exchange, this exchange will NEVER ask KYC.
ToS/AML/KYC pages are just for the state authorities to simulate compliance and not for end users.