Yes! Bitcoin is really anonymous. There are some says that Bitcoin should spread and become well-known. But there are also some who wants to hide bitcoins identity since there are dangers when it became popular.
That would really depend on the type of wallet that you are using as well as the application because cryptocurrency centralized exchanges tend to verify the identity of its customer implementing the KYC policy before the full usage of its wallet and exchange, some of them even requiring the customers social media accounts and ID's for a certain functions to activate, but if you are using wallets that you own private keys, your identity will be anonymous but the transparency of the transaction is still there.