Marker name/title/description

I'm guessing that you either want to:

• know of a website that allows users to add markers to a map created from OSM data

or

• create a website like that yourself.

If it's the first of these, then have a look a Mapquest Open. There's a feature on there called "My Maps" that may do what you want (although unfortunately "My Maps" seems to be down at the moment).

If it's the second, then the easiest place to start is probably here. That explains how to use the Leaflet javascript library to display a slippy map similar to the ones on the OpenStreetMap and Mapquest Open front pages, but with the ability to display markers. You could also do something similar with OpenLayers.