To maintain a good level of anonymity while surfing, do not log into any user accounts, do not access websites via HTTP (or mixed content), and clear your cookies before enabling a VPN service. However, any application which can query your operating system (such as Java applet, Adobe Flash, a computer program, or phone app) is likely collecting and sending identifiable information regardless of VPN. Therefore, as soon as you activate a VPN on your smartphone, which is always logged into your Google or Apple account, it will leak and associate your IP/MAC/IMEI or other identifiable information with your Google/Apple/Facebook/etc account in the background. Remaining completely anonymous on a smartphone, realistically, is almost impossible, unless you don't have a sim card, haven't activated the phone, and never added an account on the phone. However, you do not need 100% anonymity to benefit greatly from encryption and other security benefits.