Unfortunately, there is no such thing as being anonymous online. Nevertheless, a VPN does offer you privacy & security and makes it extremely hard for anyone to decipher your activities. However, the only way to be 100% anonymous digitally is not only to never use the internet but also to never use any services that may store information about you online. For most of us, that’s impossible.
A good VPN provider will only have minimal data about you (such as your email address), will not keep any activity or connection logs, will not log your IP addresses, used bandwidth, network traffic, and similar data.