1) https://wiki.openstreetmap.org/wiki/Good_practice#Map_what's_on_the_ground
2) https://wiki.openstreetmap.org/wiki/Verifiability

If the name of a path is not posted, and that the name only exists in the head of a few people, even if those are very wise and knowledgeable locals, the name should not be put to the map.  Verifiabiliy is a core principle of a crowdsourced map.

You may be interested to use the "old_name" tag instead of "name" if you want to refer to an old colloquial name that is no longer used nowadays.

Finally, please learn how to type names properly, street or paths names in OSM are always written with proper capitalisation on names, write "Chemin des Marmiteux" and not "chemin des marmiteux".