The core purpose of a VPN is to keep your information private. While browsing the internet using a VPN, third parties will not be able to see what you are doing online. Your history will not be trackable at the network-level. However, keep in mind that if someone physically accesses your computer, your browser may store your browsing history (depending on your settings). But third-parties or hackers at places like coffee shops, hotels, airports, and other public places will not be able to see or steal your data. Network administrators at home or the office will not be able to either (unless they gain physical access to your browser on your device).
If you want to keep your browsing history private on your device, it's important to either clear your browsing history every so often, or use a "private browsing" or "incognito" mode in your browser.