@Cameron Knight When you put your property into an LLC, you would be looking at commercial lending structures. Residential lending options usually require you to purchase in your name. You can purchase an investment property in your name and protect yourself by putting an umbrella insurance policy in place. Many investors purchase in their name for the financing ease and then shield everything under an umbrella, which can be a very cost effective way to create asset protection. Umbrellas are available from nearly every insurance agency and are extremely common for investors.
On the commercial side, refinancing is more difficult and costly so the BRRR really works best with residential loans. However, I have seen people buy a property under their name, BRRR it but refinance it under an LLC and put a commercial loan on it once done. When the work is complete and its stable, commercial lending isn't as prohibitive. There are many options and its really a matter of understanding the costs and hurdles to each so that you know going into the deal exactly how to hit all of your milestones.
I wish you the best of luck on your search. My wife and I are both from Southern New Hampshire (Manchester and Portsmouth) and understand how expensive those markets have gotten. If I can help in any way then please let me know.