If I am only buying and holding performing notes for cash flow, and using a servicing company, is there any benefit to purchasing/holding the notes in an LLC instead of my own name?

Anonymity. Documents get recorded with the county and are public record, I'd rather have "XZY LLC" available to the public than my actual name. Granted it's not that difficult to figure out who an LLC is registered to if one wanted to find out. There are techniques to make it difficult if you are so inclined to take the extra steps required.

Protection as well. Buying notes in an LLC protects you and separates YOU from your LLC. Investing SDIRA money in an LLC is also a good idea. I’m not the expert on the matter but what I do know I’ve learned from @Scott Carson through his training and podcast, note closers podcast.

@Rick S.

There are some advantages as notes above, but the $800/year California Franchise Tax is a real down-side for you.  Even if you are not investing in notes in CA, your CA residency creates a nexus that California may go after.  There are alternate vehicles such as trusts that would work better in your case.  Have a separate entity for investing is beneficial.

@Tim S.

Notes don't have a lot of liability therefore I don't feel an entity such as an LLC is warranted. However, if the note defaults and you have to foreclose then move the note/foreclosure/property to an entity to provide the liability protection you want.

@Scott Carson is doing his famous Note Camp this week - they always have a lot of great info, including asset protection/privacy strategies and best practices in employing them.

I agree with @Brian Eastman 's comment about CA franchise tax, it will erode your net profits on those notes. You may want to create a Personal Property Trust with you as beneficiary and have the notes assigned to the trust(s). This way the trust shows up on the county records as the lender rather than you personally. A trust does not provide any asset protection, just a level of anonymity to the borrower and the rest of the world. 

Found a discussion on BP here: https://www.biggerpockets.com/forums/52/topics/620...

It seems that the only benefit to buying and holding performing notes in an LLC is annonimity, which is very important to me.

My scenario is, I plan on moving out of CA in the near future, but I'm not sure where to. I will start purchasing notes prior to my move. I will not use a SDIRA. 

Would it be wise to just setup a DE, WY, or NV LLC to hold my notes?

I will research Personal Property Trusts also.

@Rick S. Different people will tell you different things about trusts etc but if your buying performing notes most recommend starting with just an LLC (and depending upon state some allow series LLC)

With that being said - your question really should be discussed with an attorney/ planner as this is equivalent to asking what kind of car should someone buy? A person in Alaska will most likely need a different type of car than someone in Arizona. Each situation is different and should be personalized.