There is no "place" layer (with and without "=") in OSM, or matter of fact any conventional GIS concept of layers to start with.
You can, in principle, download all objects with a "place" tag, which will include nodes, ways and relations (with other word all kind of OSM objects). However you could just as well simply edit objects as you normally would and either use the search or filter functionality in JOSM to locate the objects you want to change.
You should perhaps clarify what you are trying to achieve as editing place names tens tends not to be a task suitable for neophytes.