Delaware and Indiana do not require the registration of the managers or member. Are there any other States that do not require names from public search?
Check out Nevada and Wyoming, they provide a level of anonymity for members/managers which is what I believe you are seeking. I'm not, however, positive about what you mean by "registering". There are also many nations in the Caribbean (and elsewhere in the world) which allow equity holders to remain anonymous to certain degrees. Any of the foregoing won't change your requirement to remit taxes to the IRS and to any state to which they may be due.
The above is not intended as legal advice and creates no attorney-client relationship; do not take any action or fail to take any action in reliance.