GeoNames ( geonames.org ) is a geographical data base available and accessible without cost through various Web services. (From wikipedia 'Geonames' article). It is a project separate from OpenStreetMap.
Can we use geonames ?
Geonames is not suitable as a source for OSM, Geonames data cannot be used for editing in OpenStreetMap.
Not free enough!
see e.g. https://lists.openstreetmap.org/pipermail/talk/2007-May/014038.html
From a comment on the mailing list by Andy Robinson:
- "See http://www.geonames.org/data-sources.html
- Geonames aggregates data from other sources and you will see in the list even organisations like the Ordnance Survey listed. Thus it is not possible to say whether data is or is not subject to copyright. As a source geonames is best avoided. Better to go back to the original sources that they use and try and establish if the bit of data you are looking for is available freely or not."
Are we using geonames?
When you enter just a name of a place (lake, mountain, river etc) in the search box you are likely to get one or more locations from Geonames in the results panel, appearing lower down below any Nominatim results. However, bear in mind that these geonames locations may not have been added to the OpenStreetMap, so viewing a Geonames-located place may just show a blank map; or it may have no detail. Geonames is unlikely to locate individual streets for you.
Google summer of code project
There was a Google summer of code application idea. discussion. Mailing list posts (march/april 2008) :   
GEOnet Names Server - A government database which we can use (with caveats) . There is a lot of overlap with the GeoNames dataset in fact (GeoNames was clearly based largely on GNS at least originally)