The option is Find Places | Cities. It then brings up a list of those "Near Current Location" with an option to "spell" your own.
After selecting "Find" and "Cities" on an etrex I get a choice of "Find By Name", "Nearest Containing", "Select Map" and "Change Reference". "Select Map" allows the choice of OSM's map (called "map") or the built-in one (listed as "RecreationaRoutable Highw") or "Use Best Maps" (which seems to cause Find by Name to search one and Nearest Containing the other).
Other POIs wich can also be searched for such as Find Places | Food & Drink or Find Places | Gas Station all allow me to manually enter a name without a problem
The etrex doesn't have a "Find by Name" option against these, only "Nearest Containing", and it only searches the OSM map. I guess if the Edge doesn't have a way to select the map or search for "Nearest Containing" you're a bit stuck...