If you are logged into your Google account while connected to a VPN, Google will still be able to keep a record of all of your searches, and be able to directly link them to you. This applies to Facebook, Twitter, and any other account you might be logged into. Be aware that VPN services, while they do encrypt traffic and prevent eavesdropping, do not anonymize you if you are logged in. This is especially true for smartphones, where you are always logged into at least 1 account (Apple or Google). If you want to protect your online searches, make sure you’re logged out of your accounts.