You can't take out a restraining order just because someone Googled you. You couldn't even take out a restraining order if they were looking for personal information. Unless they threatened to physically harm you, or actually did so, it would be extremely difficult to get a restraining order. You might be able to get one if they harassed you after termination to the point that it amounted to psychological abuse and interfered with your daily life, but that has to be really extensive.

Confidentiality would make it even more difficult because you could actually get in trouble for sharing communication from the client if there was no imminent threat to you.

In any case, taking out a restraining order seems like a massive overreaction to me. If you didn't feel threatened or unsafe until you found out they had Googled you, then odds are you are overreacting - unless you're treating someone convicted of violent offenses or something. For example, if you are a woman treating a serial home invasion rapist and you find out, you might be worried. Anyway, the courts are not going to restrict someone's individual freedoms based on feelings - there has to be a clear threat based on persistent actions.