If you use a commercial registered agent and somebody else (such as an attorney) to act as the incorporator/organizer, then yes, there are ways to keep your name out of the public record (and certainly internet searches) in relation to your single member LLC.
However, when it comes to filing taxes, your personal information will be required to some extent, as a single member LLC will be reported as a disregarded entity for federal tax purposes on Schedule C of your IRS Form 1040 Income Tax Return. However, this is not in the public record.
If you wish to keep your information out of the public record and maximize privacy, contact an attorney with experience in doing so. I have this specific experience, and would be happy to discuss your options with you.
This advice is for INFORMATIONAL PURPOSES only and should not be relied upon as legal advice. No attorney-client relationship shall be formed as a result of the answer above.
I agree with my colleague that there are ways to keep you name out of the public record. You should consult with a local business attorney to discuss your situation and advise you in private as to your options. Good luck.
The above "answer" is for discussion purposes only and is neither intended as legal advice nor to create an attorney-client relationship. An attorney-client relationship is not created until after an in person consultation and I agree in writing to provide representation. I am licensed solely in the state of Arizona. You should consult with a knowledgeable attorney in your jurisdiction.
It's always a good idea to contact an attorney. However, if you do not want to do that, there are LLC filing services (I often use Interstate Filings LLC, but there are many good companies). You could give them a call and discuss with them.