Patrician families in Mainz acted a little bit like nobility. With respect to names they took them from the houses they lived in, with the predicate zu/zum/zur which they increasingly dropped by the end of the 14th century. Gutenberg's family went by the name "zum Gensfleisch" until his father became known as "Gensfleisch" alone. Zur Laden was his grandmother's last name, since it was subsequently used by the Gensfleischs it can be assumed that she brought the house into the family. Gutenberg's mother is called Wirich in the newer literature but zu Gudenberg in older books. (
https://de.wikisource.org/wiki/ADB:Gutenberg,_Johannes) The use of the name Gudenberg/Gutenberg did not start until the 1420's. Based on this it makes sense to me to use Gensfleisch as LNAB.
For CLN I'm not so sure: I have not come across any document where he himself uses the name Gutenberg alone, always Gensfleisch genannt Gutenberg or just Gensfleisch. He is called Gudenberg or Gutenberg or Guttenberg in other documents where he is not signing personally. The final document, that about his death date, refers to him as Henne Gensfleisch alone. Since the last contemporary document about his death calls him Gensfleisch an argument could be made to keep that as his CLN. On the other hand, nobody today knows him under that name and he is universally known as Gutenberg and he has been called that name in contemporary documents, so for clarity's sake Gutenberg might be preferable.
As for OLN I'd go with the names he used: Gensfleisch genannt Gutenberg, Gensfleisch zur Laden genannt Gutenberg.