The idea behind the word "anonymous" is covered in full in the entry Anonymity, which explains how anonymity works, or fails to work, in payments and crypto. This page gives a short definition of the adjective.
Something is anonymous when the person behind it cannot be identified: an unsigned letter, a cash purchase, or a donation with no name attached. In crypto the word is often used loosely. Public networks such as Bitcoin record every transaction on an open blockchain, so users are better described as pseudonymous: their wallet addresses are visible even if their names are not, and blockchain analytics firms can often link the two.
Stronger anonymity is the aim of a privacy coin such as Monero, which hides senders, receivers and amounts. Regulated exchanges, by contrast, must collect identity documents under know your customer (KYC) rules, which ties accounts back to real people.