Sold rental in LLC, buy replacement rental in same LLC?

[Account Closed]

I just sold one of my rentals that was in a single-member LLC but kept the mineral rights to the property as I receive a small income from the mineral rights. I would like to change the name that the oil and gas company has on record (the LLC) to my personal name but they require a "conveyance document of record" to be filed with the county recorder's office. They will accept a quitclaim deed but wouldn't that grant the entirety of the LLC into my personal name? What if I want to buy another rental property using that same LLC? Any thoughts?

Thanks!