I only care in terms of what it suggests for Lex’s backstory - LuthorCorp is typically used when the company was founded by Lionel.
So it may suggest we’re getting “grew up wealthy” Lex instead of “self-made billionaire” Lex. But who knows. I prefer the latter backstory myself, but am honestly fine with either.
As a name alone, I’ve always preferred LuthorCorp because it just sounds more real to me lol. Like for some reason LexCorp has always sounded a bit silly to my ears (maybe because people more rarely name corporations after their first names? So when I hear this, I think “SteveCorp” or “KarenCorp” and it amuses me

). But whatever, it really doesn’t matter.