For federal taxes, your domicile is your permanent home where you actually live, regardless of any particular piece of paper. Since single-member LLCs are disregarded entities for tax purposes, if you live in Nevada and actually do the work in Nevada, the IRS will consider it Nevada income, regardless of the registration address of the LLC. Nevada will also probably consider it in-state taxable income since single member LLCs are disregarded entities. LLCs are created under state law only, which is why the IRS does not recognize them or give them separate tax status. (An S- or C-corp is a federal creation, but LLCs are state creations so a single member LLC is a disregarded entity and a multi-member LLC is taxed the same as a simple partnership.)
I can't directly comment on California law regarding LLCs. It would certainly seem that if there is a chance that CA will consider this CA income because of the registration, even if you live and work out of state, then you would get double-taxed on the income. Certainly you would have to pay the CA business fee which I think is $800 per year? You would need to speak to an attorney about the pros and cons of closing the CA LLC and opening a new LLC in Nevada or simply going as a sole prop in Nevada. (Either way, you need a new federal EIN, if you change the LLC structure or close it, but it's easy to get a new one.)
My guess is there is little benefit to keeping the LLC in CA if you are actually changing your permanent abode and permanent place of business to NV. But you would need to ask a local expert.
