This is entirely up to the VPN provider you choose to use. There have been instances in the past of VPN providers collecting data on their users. However, these were mainly free VPN services with no explicit "no-logging" policies.  When searching for a VPN, be careful to check the company’s website for a "no-logging" policy, third-party trust verification, and trustworthy user reviews. Thankfully, most of the major paid VPNs have clearly stated "no-logging" policies, so it's typically best to stick with one of them if you have concerns.