No, most cryptocurrency is not fully anonymous, including Bitcoin. All transactions that occur using Bitcoin are recorded and verified on a public ledger called the blockchain. Those records include wallet addresses from which cryptocurrency is sent and received. Although a wallet address doesn’t constitute an identity, in most cases, it’s not hard to figure out who the owner of a wallet is or what device that wallet is stored on. For this reason, Bitcoin and other cryptocurrencies are often considered pseudo-anonymous, or “pseudonymous” for short.
Some cryptocurrencies are more anonymous than others, such as Monero. Cryptocurrency can also be tumbled (a.k.a. “washed” or “mixed”) to better obscure the connection between sender and receiver, though such services operate in a legal grey area.