If you're talking about the shipped LUTs, those are in the package/program folders. They'd rather you not mess there.
So I simply add prefixes to organize all my LUTs. A two-digit number, space for visual clarity, then a capital letter, space, then LUT name.
01 A low-sat neut
01 B norm sat neut
01 C hi-sat neut
02 A sat rolloff low-mids up
02 B sat rolloff mids up
You get the idea.
And ... as LUTS are known among colorists as "the dumbest math out there" ... and will clip without compunction ... I always follow the proper advice to apply LUTs after a 'trim node' ... so I never ever apply LUTs in the Basic tab unless it's in a second or later instance of Lumetri ... well, about ever.
I apply LUTs from the Creative tab, use the Basic tab to trim the tonal range into what the LUT needs to "see" to work correctly.