The primary request needs to go to the Lesotho government, as they will have to release the maps under a licence that is compatible with use in OSM. OSM cannot use arbitrary paper maps as a source.

Once you have the necessary intellectual rights clearances, the most expedient way of adding names would be to do so yourself. OSM operates on volunteer effort, and what gets mapped depends on the personal interests of the people who do the mapping. (There are some projects that target areas that require humanitarian assistance.)